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  Subjects -> STATISTICS (Total: 130 journals)
Showing 1 - 151 of 151 Journals sorted alphabetically
Advances in Complex Systems     Hybrid Journal   (Followers: 11)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 62)
Annals of Applied Statistics     Full-text available via subscription   (Followers: 39)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Argumentation et analyse du discours     Open Access   (Followers: 11)
Asian Journal of Mathematics & Statistics     Open Access   (Followers: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 4)
Australian & New Zealand Journal of Statistics     Hybrid Journal   (Followers: 13)
Bernoulli     Full-text available via subscription   (Followers: 9)
Biometrical Journal     Hybrid Journal   (Followers: 11)
Biometrics     Hybrid Journal   (Followers: 52)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Building Simulation     Hybrid Journal   (Followers: 2)
Bulletin of Statistics     Full-text available via subscription   (Followers: 4)
CHANCE     Hybrid Journal   (Followers: 5)
Communications in Statistics - Simulation and Computation     Hybrid Journal   (Followers: 9)
Communications in Statistics - Theory and Methods     Hybrid Journal   (Followers: 11)
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 37)
Current Research in Biostatistics     Open Access   (Followers: 8)
Decisions in Economics and Finance     Hybrid Journal   (Followers: 11)
Demographic Research     Open Access   (Followers: 15)
Electronic Journal of Statistics     Open Access   (Followers: 8)
Engineering With Computers     Hybrid Journal   (Followers: 5)
Environmental and Ecological Statistics     Hybrid Journal   (Followers: 7)
ESAIM: Probability and Statistics     Full-text available via subscription   (Followers: 5)
Extremes     Hybrid Journal   (Followers: 2)
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 9)
Geneva Papers on Risk and Insurance - Issues and Practice     Hybrid Journal   (Followers: 13)
Handbook of Numerical Analysis     Full-text available via subscription   (Followers: 5)
Handbook of Statistics     Full-text available via subscription   (Followers: 7)
IEA World Energy Statistics and Balances -     Full-text available via subscription   (Followers: 2)
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Quality, Statistics, and Reliability     Open Access   (Followers: 17)
International Journal of Stochastic Analysis     Open Access   (Followers: 3)
International Statistical Review     Hybrid Journal   (Followers: 13)
International Trade by Commodity Statistics - Statistiques du commerce international par produit     Full-text available via subscription  
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 4)
Journal of Applied Statistics     Hybrid Journal   (Followers: 21)
Journal of Biopharmaceutical Statistics     Hybrid Journal   (Followers: 21)
Journal of Business & Economic Statistics     Full-text available via subscription   (Followers: 39, SJR: 3.664, CiteScore: 2)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Computational & Graphical Statistics     Full-text available via subscription   (Followers: 20)
Journal of Econometrics     Hybrid Journal   (Followers: 84)
Journal of Educational and Behavioral Statistics     Hybrid Journal   (Followers: 6)
Journal of Forecasting     Hybrid Journal   (Followers: 17)
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Interactive Marketing     Hybrid Journal   (Followers: 10)
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Nonparametric Statistics     Hybrid Journal   (Followers: 6)
Journal of Probability and Statistics     Open Access   (Followers: 10)
Journal of Risk and Uncertainty     Hybrid Journal   (Followers: 33)
Journal of Statistical and Econometric Methods     Open Access   (Followers: 5)
Journal of Statistical Physics     Hybrid Journal   (Followers: 13)
Journal of Statistical Planning and Inference     Hybrid Journal   (Followers: 8)
Journal of Statistical Software     Open Access   (Followers: 21, SJR: 13.802, CiteScore: 16)
Journal of the American Statistical Association     Full-text available via subscription   (Followers: 72, SJR: 3.746, CiteScore: 2)
Journal of the Korean Statistical Society     Hybrid Journal   (Followers: 1)
Journal of the Royal Statistical Society Series C (Applied Statistics)     Hybrid Journal   (Followers: 33)
Journal of the Royal Statistical Society, Series A (Statistics in Society)     Hybrid Journal   (Followers: 27)
Journal of the Royal Statistical Society, Series B (Statistical Methodology)     Hybrid Journal   (Followers: 43)
Journal of Theoretical Probability     Hybrid Journal   (Followers: 3)
Journal of Time Series Analysis     Hybrid Journal   (Followers: 16)
Journal of Urbanism: International Research on Placemaking and Urban Sustainability     Hybrid Journal   (Followers: 30)
Law, Probability and Risk     Hybrid Journal   (Followers: 8)
Lifetime Data Analysis     Hybrid Journal   (Followers: 7)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Measurement Interdisciplinary Research and Perspectives     Hybrid Journal   (Followers: 1)
Metrika     Hybrid Journal   (Followers: 4)
Modelling of Mechanical Systems     Full-text available via subscription   (Followers: 1)
Monte Carlo Methods and Applications     Hybrid Journal   (Followers: 6)
Monthly Statistics of International Trade - Statistiques mensuelles du commerce international     Full-text available via subscription   (Followers: 2)
Multivariate Behavioral Research     Hybrid Journal   (Followers: 5)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 8)
Oxford Bulletin of Economics and Statistics     Hybrid Journal   (Followers: 34)
Pharmaceutical Statistics     Hybrid Journal   (Followers: 17)
Probability Surveys     Open Access   (Followers: 4)
Queueing Systems     Hybrid Journal   (Followers: 7)
Research Synthesis Methods     Hybrid Journal   (Followers: 8)
Review of Economics and Statistics     Hybrid Journal   (Followers: 128)
Review of Socionetwork Strategies     Hybrid Journal  
Risk Management     Hybrid Journal   (Followers: 15)
Sankhya A     Hybrid Journal   (Followers: 2)
Scandinavian Journal of Statistics     Hybrid Journal   (Followers: 9)
Sequential Analysis: Design Methods and Applications     Hybrid Journal  
Significance     Hybrid Journal   (Followers: 7)
Sociological Methods & Research     Hybrid Journal   (Followers: 38)
SourceOCDE Comptes nationaux et Statistiques retrospectives     Full-text available via subscription  
SourceOCDE Statistiques : Sources et methodes     Full-text available via subscription  
SourceOECD Bank Profitability Statistics - SourceOCDE Rentabilite des banques     Full-text available via subscription   (Followers: 1)
SourceOECD Insurance Statistics - SourceOCDE Statistiques d'assurance     Full-text available via subscription   (Followers: 2)
SourceOECD Main Economic Indicators - SourceOCDE Principaux indicateurs economiques     Full-text available via subscription   (Followers: 1)
SourceOECD Measuring Globalisation Statistics - SourceOCDE Mesurer la mondialisation - Base de donnees statistiques     Full-text available via subscription  
SourceOECD Monthly Statistics of International Trade     Full-text available via subscription   (Followers: 1)
SourceOECD National Accounts & Historical Statistics     Full-text available via subscription  
SourceOECD OECD Economic Outlook Database - SourceOCDE Statistiques des Perspectives economiques de l'OCDE     Full-text available via subscription   (Followers: 2)
SourceOECD Science and Technology Statistics - SourceOCDE Base de donnees des sciences et de la technologie     Full-text available via subscription  
SourceOECD Statistics Sources & Methods     Full-text available via subscription   (Followers: 1)
SourceOECD Taxing Wages Statistics - SourceOCDE Statistiques des impots sur les salaires     Full-text available via subscription  
Stata Journal     Full-text available via subscription   (Followers: 9)
Statistica Neerlandica     Hybrid Journal   (Followers: 1)
Statistical Applications in Genetics and Molecular Biology     Hybrid Journal   (Followers: 5)
Statistical Communications in Infectious Diseases     Hybrid Journal  
Statistical Inference for Stochastic Processes     Hybrid Journal   (Followers: 3)
Statistical Methodology     Hybrid Journal   (Followers: 7)
Statistical Methods and Applications     Hybrid Journal   (Followers: 6)
Statistical Methods in Medical Research     Hybrid Journal   (Followers: 27)
Statistical Modelling     Hybrid Journal   (Followers: 19)
Statistical Papers     Hybrid Journal   (Followers: 4)
Statistical Science     Full-text available via subscription   (Followers: 13)
Statistics & Probability Letters     Hybrid Journal   (Followers: 13)
Statistics & Risk Modeling     Hybrid Journal   (Followers: 3)
Statistics and Computing     Hybrid Journal   (Followers: 13)
Statistics and Economics     Open Access   (Followers: 1)
Statistics in Medicine     Hybrid Journal   (Followers: 196)
Statistics, Politics and Policy     Hybrid Journal   (Followers: 6)
Statistics: A Journal of Theoretical and Applied Statistics     Hybrid Journal   (Followers: 15)
Stochastic Models     Hybrid Journal   (Followers: 3)
Stochastics An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Reports     Hybrid Journal   (Followers: 2)
Structural and Multidisciplinary Optimization     Hybrid Journal   (Followers: 12)
Teaching Statistics     Hybrid Journal   (Followers: 7)
Technology Innovations in Statistics Education (TISE)     Open Access   (Followers: 2)
TEST     Hybrid Journal   (Followers: 3)
The American Statistician     Full-text available via subscription   (Followers: 23)
The Annals of Applied Probability     Full-text available via subscription   (Followers: 8)
The Annals of Probability     Full-text available via subscription   (Followers: 10)
The Annals of Statistics     Full-text available via subscription   (Followers: 34)
The Canadian Journal of Statistics / La Revue Canadienne de Statistique     Hybrid Journal   (Followers: 11)
Wiley Interdisciplinary Reviews - Computational Statistics     Hybrid Journal   (Followers: 1)

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Journal Cover
Journal of Theoretical Probability
Journal Prestige (SJR): 0.981
Citation Impact (citeScore): 1
Number of Followers: 3  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9230 - ISSN (Online) 0894-9840
Published by Springer-Verlag Homepage  [2656 journals]
  • Weak Convergence of Topological Measures
    • Abstract: Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and correspond to (nonlinear in general) functionals that are linear on singly generated subalgebras or singly generated cones of functions. They lack subadditivity, and many standard techniques of measure theory and functional analysis do not apply to them. Nevertheless, we show that many classical results of probability theory hold for topological and deficient topological measures. In particular, we prove a version of Aleksandrov’s theorem for equivalent definitions of weak convergence of deficient topological measures. We also prove a version of Prokhorov’s theorem which relates the existence of a weakly convergent subsequence in any sequence in a family of topological measures to the characteristics of being a uniformly bounded in variation and uniformly tight family. We define Prokhorov and Kantorovich–Rubenstein metrics and show that convergence in either of them implies weak convergence of (deficient) topological measures on metric spaces. We also generalize many known results about various dense and nowhere dense subsets of deficient topological measures. The present paper constitutes a necessary step to further research in probability theory and its applications in the context of (deficient) topological measures and corresponding nonlinear functionals.
      PubDate: 2021-04-24
  • Moderate Deviations for Drift Parameter Estimations in Reflected
           Ornstein–Uhlenbeck Process
    • Abstract: In this paper, we study the asymptotic properties of drift parameter estimations in reflected Ornstein–Uhlenbeck process, and establish their moderate deviations in both cases with one-sided barrier and two-sided barriers. The main methods consist of regenerative process techniques and the strong Markov property, as well as moderate deviations for martingales.
      PubDate: 2021-04-19
  • Random Gap Processes and Asymptotically Complete Sequences
    • Abstract: We study a process of generating random positive integer weight sequences \(\{ W_n \}\) where the gaps between the weights \(\{ X_n = W_n - W_{n-1} \}\) are i.i.d. positive integer-valued random variables. The main result of the paper is that if the gap distribution has a moment generating function with large enough radius of convergence, then the weight sequence is almost surely asymptotically m-complete for every \(m\ge 2\) , i.e. every large enough multiple of the greatest common divisor (gcd) of gap values can be written as a sum of m distinct weights for any fixed \(m \ge 2\) . Under the weaker assumption of finite \(\frac{1}{2}\) -moment for the gap distribution, we also show the simpler result that, almost surely, the resulting weight sequence is asymptotically complete, i.e. all large enough multiples of the gcd of the possible gap values can be written as a sum of distinct weights.
      PubDate: 2021-04-02
  • Higher-Order Derivative of Self-Intersection Local Time for Fractional
           Brownian Motion
    • Abstract: We consider the existence and Hölder continuity conditions for the k-th-order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where \(k=(k_1,k_2,\ldots , k_d)\) . Moreover, we show a limit theorem for the critical case with \(H=\frac{2}{3}\) and \(d=1\) , which was conjectured by Jung and Markowsky [7].
      PubDate: 2021-04-01
  • On Azuma-Type Inequalities for Banach Space-Valued Martingales
    • Abstract: In this paper, we will study concentration inequalities for Banach space-valued martingales. Firstly, we prove that a Banach space X is linearly isomorphic to a p-uniformly smooth space ( \(1<p\le 2\) ) if and only if an Azuma-type inequality holds for X-valued martingales. This can be viewed as a generalization of Pinelis’ work on an Azuma inequality for martingales with values in 2-uniformly smooth spaces. Secondly, an Azuma-type inequality for self-normalized sums will be presented. Finally, some further inequalities for Banach space-valued martingales, such as moment inequalities for double indexed dyadic martingales and De la Peña-type inequalities for conditionally symmetric martingales, will also be discussed.
      PubDate: 2021-03-31
  • Non-integrable Stable Approximation by Stein’s Method
    • Abstract: We develop Stein’s method for \(\alpha \) -stable approximation with \(\alpha \in (0,1]\) , continuing the recent line of research by Xu (Ann Appl Probab 29(1):458–504, 2019) and Chen et al. (J Theor Probab, 2018. https://doi.org/10.1007/s10959-020-01004-1) in the case \(\alpha \in (1,2)\) . The main results include an intrinsic upper bound for the error of the approximation in a variant of Wasserstein distance that involves the characterizing differential operators for stable distributions and an application to the generalized central limit theorem. Due to the lack of first moment for the approximating sequence in the latter result, the proof strategy is significantly different from that in the integrable case. We rely on fine regularity estimates of the solution to Stein’s equation established in this paper.
      PubDate: 2021-03-30
  • A Multiplicatively Symmetrized Version of the Chung-Diaconis-Graham Random
    • Abstract: This paper considers random processes of the form \(X_{n+1}=a_nX_n+b_n\pmod p\) where p is odd, \(X_0=0\) , \((a_0,b_0), (a_1,b_1), (a_2,b_2),\ldots \) are i.i.d., and \(a_n\) and \(b_n\) are independent with \(P(a_n=2)=P(a_n=(p+1)/2)=1/2\) and \(P(b_n=1)=P(b_n=0)=P(b_n=-1)=1/3\) . This can be viewed as a multiplicatively symmetrized version of a random process of Chung, Diaconis, and Graham. This paper shows that order \((\log p)^2\) steps suffice for \(X_n\) to be close to uniformly distributed on the integers mod p for all odd p while order \((\log p)^2\) steps are necessary for \(X_n\) to be close to uniformly distributed on the integers mod p.
      PubDate: 2021-03-29
  • Limit Theorems for Conservative Flows on Multiple Stochastic Integrals
    • Abstract: We consider a stationary sequence \((X_n)\) constructed by a multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the multiple integral is non-Gaussian and infinitely divisible and has a finite variance. Some additional assumptions on the dynamical system give rise to a parameter \(\beta \in (0,1)\) quantifying the conservativity of the system. This parameter \(\beta \) together with the order of the integral determines the decay rate of the covariance of \((X_n)\) . The goal of the paper is to establish limit theorems for the partial sum process of \((X_n)\) . We obtain a central limit theorem with Brownian motion as limit when the covariance decays fast enough, as well as a non-central limit theorem with fractional Brownian motion or Rosenblatt process as limit when the covariance decays slowly enough.
      PubDate: 2021-03-29
  • Quenched Local Convergence of Boltzmann Planar Maps
    • Abstract: Stephenson (2018) established annealed local convergence of Boltzmann planar maps conditioned to be large. The present work uses results on rerooted multi-type branching trees to prove a quenched version of this limit.
      PubDate: 2021-03-26
  • Non-local Solvable Birth–Death Processes
    • Abstract: In this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.
      PubDate: 2021-03-24
  • On Decoupling in Banach Spaces
    • Abstract: We consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be approximated by a Haar-type expansion in which only the pre-specified conditional distributions appear. Moreover, we show that in our framework a progressive enlargement of the underlying filtration does not affect the decoupling properties (in particular, it does not affect the constants involved). As a special case, we deal with one-sided moment inequalities for decoupled dyadic (i.e., Paley–Walsh) martingales and show that Burkholder–Davis–Gundy-type inequalities for stochastic integrals of X-valued processes can be obtained from decoupling inequalities for X-valued dyadic martingales.
      PubDate: 2021-03-14
  • Strong Renewal Theorem and Local Limit Theorem in the Absence of Regular
    • Abstract: We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction of a semistable law with index \(\alpha \in (1/2,1]\) . In the process we obtain local limit theorems for both finite and infinite mean, that is, for the whole range \(\alpha \in (0,2)\) . We also derive the asymptotics of the renewal function for \(\alpha \in (0,1]\) .
      PubDate: 2021-03-11
  • Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian
    • Abstract: In this paper, we explore the generalized mixed fractional Brownian motion in the set-indexed framework and generalize several recent results from Miao et al. (Lecture Notes and Math, Springer, New York, 2008), Zili (J. Appl. Math. Stoch. Anal. 30:1–9, 2006) and Thale (Appl. Math. Sci. 3(28):1885–1901, 2009). We present the characterization of generalized mixed set-indexed fractional Brownian motion (gmsifBM) by flows, and we extend some selected aspects to the gmsifBM for the following issues: stationary increments, self-similarity, long-range dependence, Hölder continuity, differentiability, Hausdorff dimension, etc.
      PubDate: 2021-03-11
  • Strong Solutions of Stochastic Differential Equations with Generalized
           Drift and Multidimensional Fractional Brownian Initial Noise
    • Abstract: In this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters \(H<\frac{1}{2}.\) Here, the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a “local time variational calculus” argument.
      PubDate: 2021-03-08
  • Euclidean Travelling Salesman Problem with Location-Dependent and
           Power-Weighted Edges
    • Abstract: Consider  \(n\) nodes  \(\{X_i\}_{1 \le i \le n}\) independently distributed in the unit square  \(S,\) each according to a density  \(f\) , and let  \(K_n\) be the complete graph formed by joining each pair of nodes by a straight line segment. For every edge  \(e\) in  \(K_n\) , we associate a weight  \(w(e)\) that may depend on the individual locations of the endvertices of  \(e\) and is not necessarily a power of the Euclidean length of  \(e.\) Denoting  \(\mathrm{TSP}_n\) to be the minimum weight of a spanning cycle of  \(K_n\) corresponding to the travelling salesman problem (TSP) and assuming an equivalence condition on the weight function  \(w(\cdot ),\) we prove that  \(\mathrm{TSP}_n\) appropriately scaled and centred converges to zero almost surely and in mean as  \(n \rightarrow \infty .\) We also obtain upper and lower bound deviation estimates for  \(\mathrm{TSP}_n.\)
      PubDate: 2021-03-05
  • Theta Functions and Brownian Motion
    • Abstract: A theta function for an arbitrary connected and simply connected compact simple Lie group is defined as an infinite determinant that is naturally related to the transformation of a family of independent Gaussian random variables associated with a pinned Brownian motion in the Lie group. From this definition of a theta function, the equality of the product and the sum expressions for a theta function is obtained. This equality for an arbitrary connected and simply connected compact simple Lie group is known as a Macdonald identity which generalizes the Jacobi triple product for the elliptic theta function associated with su(2).
      PubDate: 2021-03-01
      DOI: 10.1007/s10959-019-00977-y
  • Gibbsian Representation for Point Processes via Hyperedge Potentials
    • Abstract: We consider marked point processes on the d-dimensional Euclidean space, defined in terms of a quasilocal specification based on marked Poisson point processes. We construct absolutely summable Hamiltonians in terms of hyperedge potentials in the sense of Georgii et al. (Probab Theory Relat Fields 153(3–4):643–670, 2012), which are useful in models of stochastic geometry. These potentials allow for weak non-localities and are a natural generalization of the usual physical multi-body potentials, which are strictly local. Our proof relies on regrouping arguments, which use the possibility of controlled non-localities in the class of hyperedge potentials. As an illustration, we also provide such representations for the Widom–Rowlinson model under independent spin-flip time evolution. With this work, we aim to draw a link between the abstract theory of point processes in infinite volume, the study of measures under transformations and statistical mechanics of systems of point particles.
      PubDate: 2021-03-01
      DOI: 10.1007/s10959-019-00960-7
  • On the Multifractal Analysis of Branching Random Walk on
           Galton–Watson Tree with Random Metric
    • Abstract: We consider a branching random walk \(S_nX(t)\) on a supercritical random Galton–Watson tree. We compute the Hausdorff and packing dimensions of the level set \(E(\alpha )\) of infinite branches in the boundary of tree endowed with random metric along which the average of \(S_n X(t)/n\) have a given limit point.
      PubDate: 2021-03-01
      DOI: 10.1007/s10959-019-00984-z
  • Conditioned Two-Dimensional Simple Random Walk: Green’s Function and
           Harmonic Measure
    • Abstract: We study the Doob’s h-transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green’s function of this random walk and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.
      PubDate: 2021-03-01
      DOI: 10.1007/s10959-019-00963-4
  • Large Deviation Rates for Supercritical Branching Processes with
    • Abstract: Let \(\{X_n\}_0^{\infty }\) be a supercritical branching process with immigration with offspring distribution \(\{p_j\}_0^{\infty }\) and immigration distribution \(\{h_i\}_0^{\infty }.\) Throughout this paper, we assume that \(p_0=0, p_j\ne 1\) for any \(j\ge 1\) , \(1<m=\sum _{j=0}^{\infty } jp_j<\infty ,\) and \(h_0<1\) , \(0<a=\sum _{j=0}^{\infty } jh_j<\infty .\) We first show that \(Y_n=m^{-n}(X_n-\frac{m^{n+1}-1}{m-1}a)\) is a martingale and converges to a random variable Y. Secondly, we study the rates of convergence to 0 as \(n\rightarrow \infty \) of $$\begin{aligned} P(\left Y_n-Y\right >\varepsilon ), \ \ P\left( \left \frac{X_{n+1}}{X_n}-m\right >\varepsilon \Bigg Y\ge \alpha \right) \end{aligned}$$ for \(\varepsilon >0\) and \(\alpha >0\) under various moment conditions on \(\{p_j\}_0^{\infty }\) and \(\{h_i\}_0^{\infty }.\) It is shown that the rates are always supergeometric under a finite moment generating function hypothesis.
      PubDate: 2021-03-01
      DOI: 10.1007/s10959-019-00968-z
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