Subjects -> MATHEMATICS (Total: 1013 journals)
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MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 601 - 538 of 538 Journals sorted alphabetically
Results in Mathematics     Hybrid Journal  
Results in Nonlinear Analysis     Open Access  
Review of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Reviews in Mathematical Physics     Hybrid Journal   (Followers: 1)
Revista Baiana de Educação Matemática     Open Access  
Revista Bases de la Ciencia     Open Access  
Revista BoEM - Boletim online de Educação Matemática     Open Access  
Revista Colombiana de Matemáticas     Open Access   (Followers: 1)
Revista de Ciencias     Open Access  
Revista de Educación Matemática     Open Access  
Revista de la Escuela de Perfeccionamiento en Investigación Operativa     Open Access  
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas     Partially Free  
Revista de Matemática : Teoría y Aplicaciones     Open Access   (Followers: 1)
Revista Digital: Matemática, Educación e Internet     Open Access  
Revista Electrónica de Conocimientos, Saberes y Prácticas     Open Access  
Revista Integración : Temas de Matemáticas     Open Access  
Revista Internacional de Sistemas     Open Access  
Revista Latinoamericana de Etnomatemática     Open Access  
Revista Latinoamericana de Investigación en Matemática Educativa     Open Access  
Revista Matemática Complutense     Hybrid Journal  
Revista REAMEC : Rede Amazônica de Educação em Ciências e Matemática     Open Access  
Revista SIGMA     Open Access  
Ricerche di Matematica     Hybrid Journal  
RMS : Research in Mathematics & Statistics     Open Access  
Royal Society Open Science     Open Access   (Followers: 7)
Russian Journal of Mathematical Physics     Full-text available via subscription  
Russian Mathematics     Hybrid Journal  
Sahand Communications in Mathematical Analysis     Open Access  
Sampling Theory, Signal Processing, and Data Analysis     Hybrid Journal  
São Paulo Journal of Mathematical Sciences     Hybrid Journal  
Science China Mathematics     Hybrid Journal   (Followers: 1)
Science Progress     Full-text available via subscription   (Followers: 1)
Sciences & Technologie A : sciences exactes     Open Access  
Selecta Mathematica     Hybrid Journal   (Followers: 1)
SeMA Journal     Hybrid Journal  
Semigroup Forum     Hybrid Journal   (Followers: 1)
Set-Valued and Variational Analysis     Hybrid Journal  
SIAM Journal on Applied Mathematics     Hybrid Journal   (Followers: 11)
SIAM Journal on Computing     Hybrid Journal   (Followers: 11)
SIAM Journal on Control and Optimization     Hybrid Journal   (Followers: 18)
SIAM Journal on Discrete Mathematics     Hybrid Journal   (Followers: 8)
SIAM Journal on Financial Mathematics     Hybrid Journal   (Followers: 3)
SIAM Journal on Mathematics of Data Science     Hybrid Journal   (Followers: 1)
SIAM Journal on Matrix Analysis and Applications     Hybrid Journal   (Followers: 3)
SIAM Journal on Optimization     Hybrid Journal   (Followers: 12)
Siberian Advances in Mathematics     Hybrid Journal  
Siberian Mathematical Journal     Hybrid Journal  
Sigmae     Open Access  
SILICON     Hybrid Journal  
SN Partial Differential Equations and Applications     Hybrid Journal  
Soft Computing     Hybrid Journal   (Followers: 7)
Statistics and Computing     Hybrid Journal   (Followers: 13)
Stochastic Analysis and Applications     Hybrid Journal   (Followers: 2)
Stochastic Partial Differential Equations : Analysis and Computations     Hybrid Journal   (Followers: 1)
Stochastic Processes and their Applications     Hybrid Journal   (Followers: 5)
Stochastics and Dynamics     Hybrid Journal  
Studia Scientiarum Mathematicarum Hungarica     Full-text available via subscription   (Followers: 1)
Studia Universitatis Babeș-Bolyai Informatica     Open Access  
Studies In Applied Mathematics     Hybrid Journal   (Followers: 1)
Studies in Mathematical Sciences     Open Access   (Followers: 1)
Superficies y vacio     Open Access  
Suska Journal of Mathematics Education     Open Access   (Followers: 1)
Swiss Journal of Geosciences     Hybrid Journal   (Followers: 1)
Synthesis Lectures on Algorithms and Software in Engineering     Full-text available via subscription   (Followers: 2)
Synthesis Lectures on Mathematics and Statistics     Full-text available via subscription   (Followers: 1)
Tamkang Journal of Mathematics     Open Access  
Tatra Mountains Mathematical Publications     Open Access  
Teaching Mathematics     Full-text available via subscription   (Followers: 10)
Teaching Mathematics and its Applications: An International Journal of the IMA     Hybrid Journal   (Followers: 4)
Teaching Statistics     Hybrid Journal   (Followers: 8)
Technometrics     Full-text available via subscription   (Followers: 8)
The Journal of Supercomputing     Hybrid Journal   (Followers: 1)
The Mathematica journal     Open Access  
The Mathematical Gazette     Full-text available via subscription   (Followers: 1)
The Mathematical Intelligencer     Hybrid Journal  
The Ramanujan Journal     Hybrid Journal  
The VLDB Journal     Hybrid Journal   (Followers: 2)
Theoretical and Mathematical Physics     Hybrid Journal   (Followers: 7)
Theory and Applications of Graphs     Open Access  
Topological Methods in Nonlinear Analysis     Full-text available via subscription  
Transactions of the London Mathematical Society     Open Access   (Followers: 1)
Transformation Groups     Hybrid Journal  
Turkish Journal of Mathematics     Open Access  
Ukrainian Mathematical Journal     Hybrid Journal  
Uniciencia     Open Access  
Uniform Distribution Theory     Open Access  
Unisda Journal of Mathematics and Computer Science     Open Access  
Unnes Journal of Mathematics     Open Access   (Followers: 2)
Unnes Journal of Mathematics Education     Open Access   (Followers: 2)
Unnes Journal of Mathematics Education Research     Open Access   (Followers: 1)
Ural Mathematical Journal     Open Access  
Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki     Open Access  
Vestnik St. Petersburg University: Mathematics     Hybrid Journal  
VFAST Transactions on Mathematics     Open Access   (Followers: 1)
Vietnam Journal of Mathematics     Hybrid Journal  
Vinculum     Full-text available via subscription  
Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics     Open Access   (Followers: 1)
Water SA     Open Access   (Followers: 2)
Water Waves     Hybrid Journal  
Zamm-Zeitschrift Fuer Angewandte Mathematik Und Mechanik     Hybrid Journal   (Followers: 1)
ZDM     Hybrid Journal   (Followers: 2)
Zeitschrift für angewandte Mathematik und Physik     Hybrid Journal   (Followers: 2)
Zeitschrift fur Energiewirtschaft     Hybrid Journal  
Zetetike     Open Access  

  First | 1 2 3 4     

Similar Journals
Journal Cover
Stochastics and Dynamics
Journal Prestige (SJR): 0.506
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0219-4937 - ISSN (Online) 1793-6799
Published by World Scientific Homepage  [120 journals]
  • Preface for the Special Issue in Memory of María J. Garrido-Atienza

    • Free pre-print version: Loading...

      Authors: Tomás Caraballo
      Abstract: Stochastics and Dynamics, Ahead of Print.

      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722020026
       
  • Local zero-stability of rough evolution equations

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      Authors: Robert Hesse
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We analyze the long time behavior of solutions to rough parabolic equations. More precisely, we show local exponential stability for the mild solution driven by a fractional Brownian motion with Hurst parameter [math].
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722400159
       
  • Weak mean random attractors for non-local random and stochastic
           reaction–diffusion equations

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      Authors: Rubén Caballero, Pedro Marín-Rubio, José Valero
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction–diffusion equation with a nonlinear multiplicative noise. The existence and uniqueness of solutions and weak pullback mean random attractors are also established for a deterministic non-local reaction–diffusion equations with random initial data.
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722400160
       
  • An optimal control problem for a linear SPDE driven by a multiplicative
           multifractional Brownian motion

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      Authors: Wilfried Grecksch, Hannelore Lisei
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study the existence of the solution of a linear SPDE driven by a multiplicative multifractional Brownian motion. Moreover, we study an optimal control problem with a linear quadratic objective functional involving the solution of the studied SPDE. We prove the existence and uniqueness of the optimal control.
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722400202
       
  • Stochastic n-point D-bifurcations of stochastic Lévy flows and their
           complexity on finite spaces

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      Authors: Paulo Henrique Da Costa, Michael A. Högele, Paulo R. Ruffino
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper refines the classical notion of a stochastic D-bifurcation to the respective family of n-point motions for homogeneous Markovian stochastic semiflows, such as stochastic Brownian flows of homeomorphisms, and their generalizations. This notion essentially detects at which level the support of the invariant measure of the k-point bifurcation has more than one connected component. Stochastic Brownian flows and their invariant measures were shown by Kunita (1990) to be rigid, in the sense of being uniquely determined by the [math]-and [math]-point motions. Hence, only stochastic n-point bifurcation of level [math] or [math] can occur. For general homogeneous stochastic Markov semiflows this turns out to be false. This paper constructs minimal examples of where this rigidity is false in general on finite space and studies the complexity of the resulting n-point bifurcations.
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722400214
       
  • The continuity, regularity and polynomial stability of mild solutions for
           stochastic 2D-Stokes equations with unbounded delay driven by tempered
           fractional Gaussian noise

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      Authors: Yarong Liu, Yejuan Wang, Tomás Caraballo
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order [math] driven by a tempered fractional Brownian motion (TFBM) [math] with [math] and [math]. First, the global existence and uniqueness of mild solutions are established by using a new technical lemma for stochastic integrals with respect to TFBM in the sense of [math]th moment. Moreover, based on the relations between the stochastic integrals with respect to TFBM and fractional Brownian motion, we show the continuity of mild solutions in the case of [math], [math] or [math], [math]. In particular, we obtain [math]th moment Hölder regularity in time and [math]th polynomial stability of mild solutions. This paper can be regarded as a first step to study the challenging model: stochastic 2D-Navier–Stokes equations with unbounded delay driven by tempered fractional Gaussian noise.
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-10T07:00:00Z
      DOI: 10.1142/S0219493722500228
       
  • Global solutions for semilinear rough partial differential equations

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      Authors: Robert Hesse, Alexandra Neamţu
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We construct global-in-time solutions for semilinear parabolic rough partial differential equations. We work on a scale of Banach spaces tailored to the controlled rough path approach and derive suitable a priori estimates of the solution which do not contain quadratic terms.
      Citation: Stochastics and Dynamics
      PubDate: 2022-05-06T07:00:00Z
      DOI: 10.1142/S0219493722400111
       
  • Quadratic variation and drift parameter estimation for the stochastic wave
           equation with space-time white noise

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      Authors: Obayda Assaad, Julie Gamain, Ciprian A. Tudor
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We study the quadratic variations (in time and in space) of the solution to the stochastic wave equation driven by the space-time white noise. We give their limit (almost surely and in [math]) and we prove that these variations satisfy, after a proper renormalization, a Central Limit Theorem. We apply the quadratic variation to define and analyze estimators for the drift parameter of the wave equation.
      Citation: Stochastics and Dynamics
      PubDate: 2022-04-29T07:00:00Z
      DOI: 10.1142/S0219493722400147
       
  • Amplitude equations for SPDEs driven by fractional additive noise with
           small hurst parameter

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      Authors: Dirk Blömker, Alexandra Neamţu
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter [math]. Close to a change of stability measured with a small parameter [math], we rely on the natural separation of time-scales and establish a simplified description of the essential dynamics. Up to an error term bounded by a power of [math] depending on the Hurst parameter we can approximate the solution of the SPDE in first order by an SDE, the so-called amplitude equation, which describes the amplitude of the dominating pattern changing stability. In second order the approximation is given by a fast infinite-dimensional Ornstein–Uhlenbeck process. To this aim, we need to establish an explicit averaging result for stochastic integrals driven by rough fractional noise for small Hurst parameters.
      Citation: Stochastics and Dynamics
      PubDate: 2022-04-23T07:00:00Z
      DOI: 10.1142/S0219493722400135
       
  • Exponential stability of stochastic systems: A pathwise approach

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      Authors: Luu Hoang Duc
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We provide a pathwise approach using semigroup technique to study the asymptotic stability for stochastic differential equations which admit a unique equilibrium. The driving noises in consideration are [math] — Hölder continuous with [math], so that the perturbed systems can be solved using rough path theory, where the rough integrals are interpreted in the Gubinelli sense for controlled rough paths. Our approach suggests an alternative method for stochastic systems with standard Brownian noises, by not using Itô formula but a relaxed isometry property of Itô stochastic integrals.
      Citation: Stochastics and Dynamics
      PubDate: 2022-04-18T07:00:00Z
      DOI: 10.1142/S0219493722400123
       
  • On a stochastic nonlocal system with discrete diffusion modeling life
           tables

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      Authors: Tomás Caraballo, Francisco Morillas, José Valero
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study a stochastic system of differential equations with nonlocal discrete diffusion. For two types of noises, we study the existence of either positive or probability solutions. Also, we analyze the asymptotic behavior of solutions in the long term, showing that under suitable assumptions they tend to a neighborhood of the unique deterministic fixed point. Finally, we perform numerical simulations and discuss the application of the results to life tables for mortality in Spain.
      Citation: Stochastics and Dynamics
      PubDate: 2022-04-18T07:00:00Z
      DOI: 10.1142/S0219493722400172
       
  • Analysis of a new stochastic Gompertz diffusion model for untreated human
           glioblastomas

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      Authors: Tuan Anh Phan, Shuxun Wang, Jianjun Paul Tian
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we analyze a new Ito stochastic differential equation model for untreated human glioblastomas. The model was the best fit of the average growth and variance of 94 pairs of a data set. We show the existence and uniqueness of solutions in the positive spatial domain. When the model is restricted in the finite domain [math], we show that the boundary point 0 is unattainable while the point [math] is reflecting attainable. We prove there is a unique ergodic stationary distribution for any non-zero noise intensity, and obtain the explicit probability density function for the stationary distribution. By using Brownian bridge, we give a representation of the probability density function of the first passage time when the diffusion process defined by a solution passes the point [math] firstly. We carry out numerical studies to illustrate our analysis. Our mathematical and numerical analysis confirms the soundness of our randomization of the deterministic model in that the stochastic model will set down to the deterministic model when the noise intensity approaches zero. We also give physical interpretation of our stochastic model and analysis.
      Citation: Stochastics and Dynamics
      PubDate: 2022-03-21T07:00:00Z
      DOI: 10.1142/S0219493722500198
       
  • The perfection of local semi-flows and local random dynamical systems with
           applications to SDEs

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      Authors: Chengcheng Ling, Michael Scheutzow, Isabell Vorkastner
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We provide a rather general perfection result for crude local semi-flows taking values in a Polish space showing that a crude semi-flow has a modification which is a (perfect) local semi-flow which is invariant under a suitable metric dynamical system. Such a (local) semi-flow induces a (local) random dynamical system (RDS). Then we show that this result can be applied to several classes of stochastic differential equations driven by semimartingales with stationary increments such as equations with locally monotone coefficients and equations with singular drift. For these examples it was previously unknown whether they generate a (local) RDS or not.
      Citation: Stochastics and Dynamics
      PubDate: 2022-03-15T07:00:00Z
      DOI: 10.1142/S021949372240010X
       
  • On the stability of mean-field stochastic differential equations with
           irregular expectation functional

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      Authors: Oussama Elbarrimi
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we consider multidimensional mean-field stochastic differential equations where the coefficients depend on the law in the form of a Lebesgue integral with respect to the measure of the solution. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application for optimal control of diffusions. Namely, we propose a result on the approximation of the solution associated to a relaxed control.
      Citation: Stochastics and Dynamics
      PubDate: 2022-03-15T07:00:00Z
      DOI: 10.1142/S0219493722500204
       
  • The limit behavior of SEIRS model in spatial grid

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      Authors: Hongjun Gao, Shuaipeng Liu, Yeyu Xiao
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.
      Citation: Stochastics and Dynamics
      PubDate: 2022-03-12T08:00:00Z
      DOI: 10.1142/S0219493722400081
       
  • Limiting behavior of FitzHugh–Nagumo equations driven by colored noise
           on unbounded thin domains

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      Authors: Lin Shi, Kening Lu, Xiaohu Wang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We investigate the limiting behavior of dynamics of non-autonomous stochastic FitzHugh–Nagumo equations driven by a nonlinear multiplicative colored noise on unbounded thin domains. We first establish the existence and uniqueness of random attractors for the equations on the thin domains and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.
      Citation: Stochastics and Dynamics
      PubDate: 2022-03-12T08:00:00Z
      DOI: 10.1142/S0219493722400093
       
  • Optimal index and averaging principle for Itô–Doob stochastic
           fractional differential equations

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      Authors: Wenya Wang, Zhongkai Guo
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, a class of Itô–Doob stochastic fractional differential equations (Itô–Doob SFDEs) models are discussed. Using the time scale transformation method, we consider the averaging principle of the transformed equations and establish the relevant results. At the same time, we find that the optimal index for the original Itô–Doob SFDEs can be determined, the selection of such index is similar to the classical stochastic differential equations model.
      Citation: Stochastics and Dynamics
      PubDate: 2022-02-25T08:00:00Z
      DOI: 10.1142/S0219493722500186
       
  • Strong rates of convergence of space-time discretization schemes for the
           2D Navier–Stokes equations with additive noise

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      Authors: Hakima Bessaih, Annie Millet
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We consider the strong solution of the 2D Navier–Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the space-time rate of convergence is the “optimal” one, namely, [math] in time and 1 in space. Let us mention that the coefficient [math] is equal to the time regularity of the solution with values in [math]. Our method relies on the existence of finite exponential moments for both the solution and its time approximation. Unlike previous results, our main new idea is the use of a discrete Grönwall lemma for the error estimate without any localization.
      Citation: Stochastics and Dynamics
      PubDate: 2022-01-26T08:00:00Z
      DOI: 10.1142/S0219493722400056
       
  • Stochastic 2D rotating Euler flows with bounded vorticity or white noise
           initial conditions

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      Authors: Hongjun Gao, Xiancheng Gao
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we consider the stochastic two-dimensional (2D) rotating Euler equations with [math] initial conditions and white noise initial conditions, respectively. The existence and uniqueness of the equations with [math] vorticity are proved. The stability of [math] tending to 0 for [math] initial conditions will be proved. At last, the case of white noise initial conditions is considered.
      Citation: Stochastics and Dynamics
      PubDate: 2022-01-26T08:00:00Z
      DOI: 10.1142/S021949372240007X
       
  • A stochastic Sir epidemic evolution model with non-concave force of
           infection: Mathematical modeling and analysis

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      Authors: A. Lahrouz, A. Settati, M. Jarroudi, H. Mahjour, M. Fatini, M. Merzguioui, A. Tridane
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we revisit the classical SIR epidemic model by replacing the simple bilinear transmission rate by a nonlinear one. Our results show that in the presence of environmental fluctuations represented by Brownian motion and that mainly act on the transmission rate, the generalized non-concave force of infection adopted here, greatly affects the long-time behavior of the epidemic. Employing the Markov semigroup theory, we prove that the model solutions do not admit a unique stationary distribution but converge to 0 in [math]th moment for any [math]. Furthermore, we prove that the disease extinguishes asymptotically exponentially with probability 1 without any restriction on the model parameters and we also determine the rate of convergence. This is an unexpected qualitative behavior in comparison with the existing literature where the studied epidemic models have a threshold dynamics behavior. It is also a very surprising behavior regarding the deterministic counterpart that can exhibit a rich qualitative dynamical behaviors such as backward bifurcation and Hopf bifurcation. On the other hand, we show by several numerical simulations that as the intensity of environmental noises becomes sufficiently small, the epidemic tends to persist for a very long time before dying out from the host population. To solve this problem and to be able to manage the pre-extinction period, we construct a new process in terms of the number of infected and recovered individuals which admits a unique invariant stationary distribution. Finally, we discuss the obtained analytical results through a series of numerical simulations.
      Citation: Stochastics and Dynamics
      PubDate: 2022-01-26T08:00:00Z
      DOI: 10.1142/S0219493722500162
       
  • Existence of solutions for mean-field integrodifferential equations with
           delay

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      Authors: Moustapha Dieye, Amadou Diop, Mark A. Mckibben
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study the existence and continuous dependence on coefficients of mild solutions for first-order McKean–Vlasov integrodifferential equations with delay driven by a cylindrical Wiener process using resolvent operator theory and Wasserstein distance. Under the situation that the nonlinear term depends on the probability distribution of the state, the existence and uniqueness of solutions are established. An example illustrating the general results is included.
      Citation: Stochastics and Dynamics
      PubDate: 2022-01-26T08:00:00Z
      DOI: 10.1142/S0219493722500174
       
  • Attractors of deterministic and random lattice difference equations

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      Authors: Peter E. Kloeden
      Abstract: Stochastics and Dynamics, Ahead of Print.
      Lattice difference equations are essentially difference equations on a Hilbert space of bi-infinite sequences. They are motivated by the discretization of the spatial variable in integrodifference equations arising in theoretical ecology. It is shown here that under similar assumptions to those used for such integrodifference equations they have a global attractor, to which the global attractors of finite-dimensional approximations converge upper-semi-continuously. Corresponding results are also shown for the lattice difference equations when only a finite number of interconnection weights are nonzero and when the interconnection weights themselves vary and converge in an appropriate manner.
      Citation: Stochastics and Dynamics
      PubDate: 2022-01-20T08:00:00Z
      DOI: 10.1142/S0219493722400068
       
  • Existence and uniqueness of global solutions to the stochastic heat
           equation with superlinear drift on an unbounded spatial domain

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      Authors: Michael Salins
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We prove the existence and uniqueness of global solutions to the semilinear stochastic heat equation on an unbounded spatial domain with forcing terms that grow superlinearly and satisfy an Osgood condition [math] along with additional restrictions. For example, consider the forcing [math]. A new dynamic weighting procedure is introduced to control the solutions, which are unbounded in space.
      Citation: Stochastics and Dynamics
      PubDate: 2021-12-28T08:00:00Z
      DOI: 10.1142/S0219493722500149
       
  • Invariant measures for random expanding on average Saussol maps

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      Authors: Fawwaz Batayneh, Cecilia González-Tokman
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for random expanding on average Saussol maps in higher dimensions. This is done by the establishment of a random Lasota–Yorke inequality for the transfer operators on the space of bounded oscillation. We prove that the number of ergodic skew product ACIPs is finite and will provide an upper bound for the number of these ergodic ACIPs. This work can be seen as a generalization of the work in [F. Batayneh and C. González-Tokman, On the number of invariant measures for random expanding maps in higher dimensions, Discrete Contin. Dyn. Syst. 41 (2021) 5887–5914] on admissible random Jabłoński maps to a more general class of higher-dimensional random maps.
      Citation: Stochastics and Dynamics
      PubDate: 2021-12-28T08:00:00Z
      DOI: 10.1142/S0219493722500150
       
  • Stochastic turbulence for Burgers equation driven by cylindrical Lévy
           process

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      Authors: Shenglan Yuan, Dirk Blömker, Jinqiao Duan
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [math] tends towards zero. The inviscid limit describes the strong stochastic turbulence.
      Citation: Stochastics and Dynamics
      PubDate: 2021-12-22T08:00:00Z
      DOI: 10.1142/S0219493722400044
       
  • Nonautonomous attractors and Young measures

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      Authors: Franco Flandoli, Umberto Pappalettera, Elisa Tonello
      Abstract: Stochastics and Dynamics, Ahead of Print.
      Motivated by the problem of identifying a mathematical framework for the formal definition of concepts such as weather, climate and connections between them, we discuss a question of convergence of short-time time averages for random nonautonomous dynamical systems depending on a parameter. The problem is formulated by means of Young measures. Using the notion of pull-back attractor, we prove a general theorem giving a sufficient condition for the tightness of the law of the approximating problems. In a specific example, we show that the theorem applies and we characterize the unique limit point.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-30T08:00:00Z
      DOI: 10.1142/S0219493722400032
       
  • A probabilistic numerical method for a class of mean field games

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      Authors: Ben Aziza Sahar, Toumi Salwa
      Abstract: Stochastics and Dynamics, Ahead of Print.
      The Mean Field Games PDEs system is at the heart of the Mean Field Games theory initiated by [J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I–le cas stationnaire, C. R. Math. 343 (2006) 619–625; J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II–horizon fini et contrôle optimal, C. R. Math. 343 (2006) 679–684; J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math. 2 (2007) 229–260] which constitutes a seminal contribution to the modeling and analysis of games with a large number of players. We propose here a numerical method of resolution of such systems based on the construction of a discrete mean field game where the controlled state-variable is a Markov chain approximating the controlled stochastic differential equation [H. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Stochastic Modeling and Applied Probability, Vol. 24 (Springer Science & Business Media, 2013)]. In particular, existence and uniqueness properties of the discrete MFG are investigated with convergence results under adequate assumptions.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-30T08:00:00Z
      DOI: 10.1142/S0219493722500083
       
  • Study of the dynamics of two chemostats connected by Fickian diffusion
           with bounded random fluctuations

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      Authors: Tomás Caraballo, Javier López-de-la-Cruz, Alain Rapaport
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-24T08:00:00Z
      DOI: 10.1142/S0219493722400020
       
  • Reflected and doubly reflected BSDEs driven by RCLL martingales

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      Authors: Tianyang Nie, Marek Rutkowski
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu [BSDEs with random default time and their applications to default risk, working paper, preprint (2009), arXiv:0910.2091] and Dumitrescu et al. [BSDEs with default jump, in Computation and Combinatorics in Dynamics, Stochastics and Control, Abel Symposia, Vol. 13, eds. E. Celledoni, G. Di Nunno, K. Ebrahimi-Fard and H. Munthe-Kaas (Springer, Cham, 2018), pp. 233–263] who examined BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-17T08:00:00Z
      DOI: 10.1142/S0219493722500125
       
  • On the weak invariance principle for non-adapted stationary random fields
           under projective criteria

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      Authors: Han-Mai Lin
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study the central limit theorem (CLT) and its weak invariance principle (WIP) for sums of stationary random fields non-necessarily adapted, under different normalizations. To do so, we first state sufficient conditions for the validity of a suitable ortho-martingale approximation. Then, with the help of this approximation, we derive projective criteria under which the CLT as well as the WIP hold. These projective criteria are in the spirit of Hannan’s condition and are well adapted to linear random fields with ortho-martingale innovations and which exhibit long memory.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-13T08:00:00Z
      DOI: 10.1142/S0219493722500137
       
  • Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward
           processes

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      Authors: Adrien Barrasso, Francesco Russo
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We are interested in path-dependent semilinear PDEs, where the derivatives are of Gâteaux type in specific directions [math] and [math], being the kernel functions of a Volterra Gaussian process [math]. Under some conditions on [math] and the coefficients of the PDE, we prove existence and uniqueness of a decoupled mild solution, a notion introduced in a previous paper by the authors. We also show that the solution of the PDE can be represented through BSDEs where the forward (underlying) process is [math].
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-06T07:00:00Z
      DOI: 10.1142/S0219493722500071
       
  • Regularity for distribution-dependent SDEs driven by jump processes

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      Authors: Yulin Song, Zengwu Wang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, the following [math]-dimensional distribution-dependent stochastic differential equation driven by a pure jump process is studied: Xtξ = ξ +∫0tb(X s−ξ,μ s)ds +∫0t∫B0σ(Xs−ξ,z,μ s)N ̂(dz,ds),t ∈ [0, 1], where [math] denotes the distribution of [math]. The differentiability of the map [math] is investigated in the sense of [math]. By the Malliavin calculus for jump processes, the following Bismut type derivative formula is established, ∇η𝔼f(Xtξ) = 𝔼(f(X tξ)M tξ), where [math] is a test function and [math] is a random variable depending on the initial value [math]. Sharp gradient estimates in short time are also obtained.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-06T07:00:00Z
      DOI: 10.1142/S0219493722500113
       
  • An averaging principle for neutral stochastic fractional order
           differential equations with variable delays driven by Lévy noise

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      Authors: Guangjun Shen, Jiang-Lun Wu, Ruidong Xiao, Xiuwei Yin
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we establish an averaging principle for neutral stochastic fractional differential equations with non-Lipschitz coefficients and with variable delays, driven by Lévy noise. Our result shows that the solutions of the equations concerned can be approximated by the solutions of averaged neutral stochastic fractional differential equations in the sense of convergence in mean square. As an application, we present an example with numerical simulations to explore the established averaging principle.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-03T07:00:00Z
      DOI: 10.1142/S0219493722500095
       
  • Synchronization for KPZ

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      Authors: Tommaso C. Rosati
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We study the long-time behavior of Kardar–Parisi–Zhang (KPZ)-like equations: ∂th(t,x) = Δxh(t,x) + ∇xh(t,x) 2 + η(t,x), h(0,x) = h0(x), (t,x) ∈ (0,∞) × ð•‹d, on the [math]-dimensional torus [math] driven by an ergodic noise [math] (e.g., space-time white in [math]). The analysis builds on infinite-dimensional extensions of similar results for positive random matrices. We establish a one force, one solution principle and derive almost sure synchronization with exponential deterministic speed in appropriate Hölder spaces.
      Citation: Stochastics and Dynamics
      PubDate: 2021-11-03T07:00:00Z
      DOI: 10.1142/S0219493722500101
       
  • Attractors for multi-valued lattice dynamical systems with nonlinear
           diffusion terms

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      Authors: Panpan Zhang, Anhui Gu
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.
      Citation: Stochastics and Dynamics
      PubDate: 2021-10-09T07:00:00Z
      DOI: 10.1142/S021949372140013X
       
  • Wong–Zakai approximations and limiting dynamics of stochastic
           Ginzburg–Landau equations

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      Authors: Ji Shu, Dandan Ma, Xin Huang, Jian Zhang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper deals with the Wong–Zakai approximations and random attractors for stochastic Ginzburg–Landau equations with a white noise. We first prove the existence of a pullback random attractor for the approximate equation under much weaker conditions than the original stochastic equation. In addition, when the stochastic Ginzburg–Landau equation is driven by an additive white noise, we establish the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation tends to zero.
      Citation: Stochastics and Dynamics
      PubDate: 2021-10-08T07:00:00Z
      DOI: 10.1142/S021949372250006X
       
  • Large deviation principles for a 2D stochastic
           Allen–Cahn–Navier–Stokes driven by jump noise

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      Authors: Theodore Tachim Medjo
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we derive a large deviation principle for a stochastic 2D Allen–Cahn–Navier–Stokes system with a multiplicative noise of Lévy type. The model consists of the Navier–Stokes equations for the velocity, coupled with a Allen–Cahn system for the order (phase) parameter. The proof is based on the weak convergence method introduced in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. Henri Poincarà ⓒ Probab. Stat. 47(3) (2011) 725–747].
      Citation: Stochastics and Dynamics
      PubDate: 2021-09-30T07:00:00Z
      DOI: 10.1142/S0219493722500058
       
  • Talagrand’s quadratic transportation cost inequalities for SPDEs driven
           by fractional noises with two reflection walls

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      Authors: Yumeng Li
      Abstract: Stochastics and Dynamics, Ahead of Print.
      Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for the laws of the solutions of stochastic partial differential equations (SPDEs) with two reflection walls under the uniform norm on the continuous functions space. These equations are driven by fractional noises.
      Citation: Stochastics and Dynamics
      PubDate: 2021-09-10T07:00:00Z
      DOI: 10.1142/S0219493722500046
       
  • Weak pullback mean random attractors for stochastic evolution equations
           and applications

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      Authors: Anhui Gu
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction–diffusion equations, the stochastic [math]-Laplace equation and stochastic porous media equations are established.
      Citation: Stochastics and Dynamics
      PubDate: 2021-09-09T07:00:00Z
      DOI: 10.1142/S0219493722400019
       
  • Limit measures and ergodicity of fractional stochastic
           reaction–diffusion equations on unbounded domains

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      Authors: Zhang Chen, Bixiang Wang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.
      Citation: Stochastics and Dynamics
      PubDate: 2021-09-04T07:00:00Z
      DOI: 10.1142/S0219493721400128
       
  • Reflected stochastic partial differential equations with jumps

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      Authors: Hongchao Qian, Jun Peng
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we establish the existence and uniqueness of solutions of reflected stochastic partial differential equations (SPDEs) driven both by Brownian motion and by Poisson random measure in a convex domain. Penalization method plays a crucial role.
      Citation: Stochastics and Dynamics
      PubDate: 2021-08-28T07:00:00Z
      DOI: 10.1142/S0219493722500022
       
  • The non-Lipschitz stochastic Cahn–Hilliard–Navier–Stokes equations
           in two space dimensions

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      Authors: Chengfeng Sun, Qianqian Huang, Hui Liu
      Abstract: Stochastics and Dynamics, Ahead of Print.
      The stochastic two-dimensional Cahn–Hilliard–Navier–Stokes equations under non-Lipschitz conditions are considered. This model consists of the Navier–Stokes equations controlling the velocity and the Cahn–Hilliard model controlling the phase parameters. By iterative techniques, a priori estimates and weak convergence method, the existence and uniqueness of an energy weak solution to the equations under non-Lipschitz conditions have been obtained.
      Citation: Stochastics and Dynamics
      PubDate: 2021-08-28T07:00:00Z
      DOI: 10.1142/S0219493722500034
       
  • On a stochastic nonclassical diffusion equation with standard and
           fractional Brownian motion

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      Authors: Tomás Caraballo, Tran Bao Ngoc, Tran Ngoc Thach, Nguyen Huy Tuan
      Abstract: Stochastics and Dynamics, Ahead of Print.
      This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case [math], where [math] is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when [math]. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm.
      Citation: Stochastics and Dynamics
      PubDate: 2021-07-15T07:00:00Z
      DOI: 10.1142/S0219493721400116
       
  • Characterization of stochastic equilibrium controls by the Malliavin
           calculus

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      Authors: Jiang Yu Nguwi, Nicolas Privault
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.
      Citation: Stochastics and Dynamics
      PubDate: 2021-07-06T07:00:00Z
      DOI: 10.1142/S0219493721500544
       
  • Higher-dimensional open quantum walk in environment of quantum Bernoulli
           noises

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      Authors: Ce Wang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.
      Citation: Stochastics and Dynamics
      PubDate: 2021-07-03T07:00:00Z
      DOI: 10.1142/S0219493722500010
       
  • Penalization for a PDE with a nonlinear Neumann boundary condition and
           measurable coefficients

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      Authors: Khaled Bahlali, Brahim Boufoussi, Soufiane Mouchtabih
      Abstract: Stochastics and Dynamics, Ahead of Print.
      We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized PDEs, which converges to our initial problem. Since the coefficients we consider may be discontinuous, we use the notion of solution in the [math]-viscosity sense. The method we use is based on backward stochastic differential equations and their [math]-tightness. This work is motivated by the fact that many PDEs in physics have discontinuous coefficients. As a consequence, it follows that if the uniqueness holds, then the solution can be constructed by a penalization.
      Citation: Stochastics and Dynamics
      PubDate: 2021-06-22T07:00:00Z
      DOI: 10.1142/S0219493721500532
       
  • Wong–Zakai approximations of second-order stochastic lattice systems
           driven by additive white noise

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      Authors: Yiju Chen, Chunxiao Guo, Xiaohu Wang
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.
      Citation: Stochastics and Dynamics
      PubDate: 2021-06-15T07:00:00Z
      DOI: 10.1142/S0219493721500507
       
  • High order Anderson parabolic model driven by rough noise in space

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      Authors: Qiyong Cao, Hongjun Gao
      Abstract: Stochastics and Dynamics, Ahead of Print.
      In this paper, we concern the fourth parabolic model on [math] driven by a multiplicative Gaussian noise which behaves like fractional Brownian motion in time and space with Hurst index [math] and [math], respectively. The existence and uniqueness of mild solution in Skorohod sense are proved, and the weak intermittency is obtained by estimating [math]th ([math]) moment of the solution. Moreover, the Hölder continuity can be obtained for the time and space variable.
      Citation: Stochastics and Dynamics
      PubDate: 2021-06-15T07:00:00Z
      DOI: 10.1142/S0219493721500520
       
  • On the geometric ergodicity for a generalized IFS with probabilities

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      Authors: Grzegorz Guzik, Rafał Kapica
      Abstract: Stochastics and Dynamics, Ahead of Print.
      Main goal of this paper is to formulate possibly simple and easy to verify criteria on existence of the unique attracting probability measure for stochastic process induced by generalized iterated function systems with probabilities (GIFSPs). To do this, we study the long-time behavior of trajectories of Markov-type operators acting on product of spaces of Borel measures on arbitrary Polish space. Precisely, we get the desired geometric rate of convergence of sequences of measures under the action of such operator to the unique distribution in the Hutchinson–Wasserstein distance. We apply the obtained results to study limiting behavior of random trajectories of GIFSPs as well as stochastic difference equations with multiple delays.
      Citation: Stochastics and Dynamics
      PubDate: 2021-06-05T07:00:00Z
      DOI: 10.1142/S0219493721500519
       
 
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