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Theory of Probability and its Applications
Journal Prestige (SJR): 0.411

Number of Followers: 2

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0040-585X - ISSN (Online) 1095-7219
Published by Society for Industrial and Applied Mathematics

[17 journals]

On the 90th Birthday of A. N. Shiryaev
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  Authors: M.V. Khatuntseva
  Pages: 507 - 507
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 507-507, February 2025.
  Recognition of the 90th birthday of leading probability specialist Albert Nikolaevich Shiryaev. He has been an active member of the Editorial Board of Theory of Probability and Its Applications for over 45 years and has served as the journal's editor-in-chief for the past 10 years. His contributions to probability theory and mathematical statistics have inspired researchers both past and present.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992082
  Issue No: Vol. 69, No. 4 (2025)
On Short Chebyshev--Edgeworth Expansions for Weighted Sums of Random
Vectors
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  Authors: S. A. Ayvazyan
  Pages: 508 - 519
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 508-519, February 2025.
  We consider “typical” asymptotic behavior of weighted sums of independent identically distributed random vectors in the $k$-dimensional space. We show that if the fifth absolute moment of a separate term is finite, then in the multidimensional central limit theorem, the convergence rate is $O(1/n^{3/2})$ under the Chebyshev--Edgeworth correction. This result generalizes a result of Bobkov [Edgeworth corrections in randomized central limit theorems, in Geometric Aspects of Functional Analysis, Springer, 2020, pp. 71--97] to the multidimensional case.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992094
  Issue No: Vol. 69, No. 4 (2025)
Martingale Methods in the Problem of Existence of Survival Strategies
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  Authors: M. V. Zhitlukhin, A. A. Tokaeva
  Pages: 520 - 530
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 520-530, February 2025.
  Dedicated to Albert Nikolaevich Shiryaev on the occasion of his 90th birthday We consider a model of a financial market with endogenous asset prices. An agent's strategy is called survival if its share of the total market wealth is bounded away from zero over the infinite time horizon regardless of the strategies used by the other agents. We obtain necessary and sufficient conditions for survival of strategies, which generalize known results that deal with construction of such strategies or only with necessary conditions for survival. The proofs rely mainly on martingale convergence theorems.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992100
  Issue No: Vol. 69, No. 4 (2025)
On Parameter Estimation of Diffusion-Type Processes: Sequential Estimation
Revisited
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  Authors: A. A. Novikov, A. N. Shiryaev, N. E. Kordzakhia
  Pages: 531 - 552
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 531-552, February 2025.
  We derive new properties of the sequential parameter estimators for diffusion-type processes $\mathbf{X}=\{X_t,\, 0\leq t\leq \tau \}$, where $\tau $ is a stopping time (this includes the case of fixed sample size estimate). Some earlier theoretical results in this direction can be found in the book [R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes, Springer, 2001]. Under an essentially less restrictive setting, we derive formulas for the moments of the maximum likelihood estimator (MLE) $\widehat{\lambda}_{\tau }$ for the parameter $\lambda $ of the drift coefficient $f_{t}(\lambda )=a_{t}-\lambda b_{t}$ and prove the exponential boundedness of $\widehat{\lambda}_{\tau }$ under a mild condition. In the provided examples we consider the mean-reverting ergodic diffusion process $\mathbf{X}$, where $b_{t}=X_{t}$, and the diffusion coefficient $\sigma_{t}=\sigma X_{t}^{\gamma }$. In particular, we provide nonasymptotic analytical and numerical results for the bias and mean-square error of $\widehat{\lambda}_{\tau }$ for the Ornstein--Uhlenbeck (O--U) and Cox--Ingersoll--Ross (CIR) processes when $\tau =T$ is a fixed sample size, and $\tau =\tau_{H}$ is a specially chosen stopping time that guarantees a prescribed magnitude of $1/H$ for the variance of $\widehat{\lambda}_{\tau_{H}}$.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992112
  Issue No: Vol. 69, No. 4 (2025)
Spectral Methods and Their Applications in Analysis of Branching Random
Walks
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  Authors: E. B. Yarovaya
  Pages: 553 - 564
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 553-564, February 2025.
  Dedicated to A. N. Shiryaev on his 90th birthday Spectral methods are widely used in stochastic analysis. We establish a link between branching random walks with signed branching sources of various intensities and the structure of the spectrum of the evolutionary operator for the mean population size of particles at the lattice points. In this connection, we solve the problem of the number of eigenvalues of a finite-dimensional non-self-adjoint perturbation $A+B$ of a non-self-adjoint operator $A$ in a real Hilbert space. We prove that the number of eigenvalues of the operator $A+B$ exceeding the upper bound of the spectrum of the operator $A$ is majorized by the number of positive eigenvalues of the operator $B$, and the number of eigenvalues of the operator $A+B$ smaller than the lower bound of the spectrum of the operator $A$ is majorized by the number of negative eigenvalues of the operator $B$.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992124
  Issue No: Vol. 69, No. 4 (2025)
Spontaneously Started Signals with White Noise
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  Authors: P. A. Yaskov
  Pages: 565 - 578
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 565-578, February 2025.
  We give a complete description of the conditions for equivalency of the distribution of Brownian motion with randomly started drift of the square root type to the Wiener measure. This problem is closely related to the theory of Gaussian multiplicative chaos (GMC). We develop a new elementary method to prove the existence of the density of the corresponding distribution, which, in fact, is related to one-dimensional GMC in the subcritical regime.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992136
  Issue No: Vol. 69, No. 4 (2025)
On the Representation Property for 1D General Diffusion Semimartingales
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  Authors: D. Criens, M. Urusov
  Pages: 579 - 591
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 579-591, February 2025.
  Dedicated to A. N. Shiryaev on his 90th birthday A general diffusion semimartingale is a one-dimensional path-continuous semimartingale that is also a regular strong Markov process. We say that a continuous semimartingale has the representation property if all local martingales w.r.t. its canonical filtration have an integral representation w.r.t. its continuous local martingale part. The representation property is of fundamental interest in the field of mathematical finance, where it is strongly connected to market completeness. The main result from this paper shows that the representation property holds for a general diffusion semimartingale (that is not started in an absorbing boundary point) if and only if its scale function is (locally) absolutely continuous on the interior of the state space. As an application of our main theorem, we deduce that the laws of general diffusion semimartingales with such scale functions are extreme points of their semimartingale problems, and, moreover, we construct a general diffusion semimartingale whose law is no extreme point of its semimartingale problem. These observations contribute to a solution of problems posed by J. Jacod and M. Yor and D. W. Stroock and M. Yor, respectively, on the extremality of strong Markov solutions.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992148
  Issue No: Vol. 69, No. 4 (2025)
New Characterizations of the Gamma Distribution via Independence of Two
Statistics by Using Anosov's Theorem
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  Authors: G. D. Lin, J. M. Stoyanov
  Pages: 592 - 604
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 592-604, February 2025.
  There are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well known is the classical result when one of the statistics is the sample mean and the other is the sample coefficient of variation. In this paper, we elaborate on a version of Anosov's theorem, which allows us to establish a general result and a series of seven corollaries, providing new characterization results for gamma distributions. We keep the sample mean as one of involved statistics, while the other can be taken from a quite large class of homogeneous feasible definite statistics. We discuss an interesting parallel between the new characterization results for gamma distributions and recent characterization results for the normal distribution.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T99215X
  Issue No: Vol. 69, No. 4 (2025)
Limiting Behaviors for Weighted Sums of $m$-WOD Random Variables under
Integrability Assumptions
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  Authors: Y. Wu, M. M. Xi, X. J. Wang
  Pages: 605 - 621
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 605-621, February 2025.
  In this work, the $L_r$-convergence for weighted sums of $R$-$h$-integrable $m$-WOD random variables, the complete convergence, complete moment convergence, and complete $f$-moment convergence for weighted sums of $SR$-$h$-integrable $m$-WOD random variables are established, which improve and generalize some previously obtained results in the literature. As an application, the weak consistency of the wavelet estimator in nonparametric regression models is obtained under very general assumptions.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992161
  Issue No: Vol. 69, No. 4 (2025)
Uniform Integrability of Nonnegative Supermartingales via Time Change in a
Geometric Brownian Motion
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  Authors: A. A. Gushchin
  Pages: 622 - 629
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 622-629, February 2025.
  Dedicated to Albert Nikolaevich Shiryaev, my teacher, on the occasion of his 90th birthday We propose a new approach to derivation of sufficient conditions for uniform integrability of nonnegative supermartingales or, equivalently, to derivation of conditions for absolute continuity of probability measures. Our approach is based on a representation of nonnegative supermartingales proposed by M. A. Urusov and the author of the present paper via a time change in a geometric Brownian motion. We prove a criterion for uniform integrability in terms of a time change and also put forward a new proof of sufficiency of the Novikov condition. It turns out that an elementary alternative proof of this fact can be reduced to its particular case for the stopped geometric Brownian motion.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992173
  Issue No: Vol. 69, No. 4 (2025)
Almost Sure Results for Generalized Normal Distribution
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  Authors: L. Wen, Z. Zhuang
  Pages: 630 - 636
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 630-636, February 2025.
  For a sequence of independent and identically generalized normal random variables, the almost sure convergence rates, which characterize the fluctuation to infinity or to some fixed point, are obtained.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992185
  Issue No: Vol. 69, No. 4 (2025)
Abstracts of Talks Given at the 9th International Conference on Stochastic
Methods
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  Authors: A. N. Shiryaev
  Pages: 637 - 669
  Abstract: Theory of Probability & Its Applications, Volume 69, Issue 4, Page 637-669, February 2025.
  This paper presents abstracts of talks given at the 9th International Conference on Stochastic Methods (ICSM-9), held June 2--8, 2024 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of Don State Technical University. The conference was chaired by A. N. Shiryaev.
  Citation: Theory of Probability & Its Applications
  PubDate: 2025-02-26T08:00:00Z
  DOI: 10.1137/S0040585X97T992197
  Issue No: Vol. 69, No. 4 (2025)

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