STOCHASTIC PROCESSES AND THEIR APPLICATIONS随机过程及其应用
STOCHASTIC PROCESSES AND THEIR APPLICATIONS(英文缩写 STOCH PROC APPL),ISSN 0304-4149,eISSN 1879-209X,中文译名:随机过程及其应用 是一本学术期刊。本页汇总该期刊的最新影响因子、分区信息以及最新收录于 PubMed 的文献,帮助您快速了解期刊全貌。
发文量统计区间：2025-11-01 至 2026-10-31，按本站收录文献的发表日期统计。
期刊介绍
历年影响因子趋势
| JCR 数据年份 | 影响因子 | JCR 分区 |
|---|---|---|
| 2021 | 1.430 | Q3 |
| 2022 | 1.400 | Q3 |
| 2023 | 1.100 | Q3 |
| 2024 | 1.200 | Q2 |
| 2025 | 1.200 | Q3 |
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 最新收录文献
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1. Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population.
PMID:日期:2025-01-11The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing population. Using branching process techniques, we establish (first-order) almost sure convergence results for the SFS of a Galton-Watson process, evaluated either at a fixed time or at the stochastic time at which the population first reaches a certain size. We finally use our results to construct consistent estimators for the extinction probability and the effective mutation rate of a birth-death process.
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2. Perturbation bounds for Monte Carlo within Metropolis via restricted approximations.
PMID:日期:2020-04The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov chain is geometrically ergodic, we show explicit estimates of the difference between the th step distributions of the perturbed MCwM and the unperturbed MH chains. These bounds are based on novel perturbation results for Markov chains which are of interest beyond the MCwM setting. To apply the bounds, we need to control the difference between the transition probabilities of the two chains and to verify stability of the perturbed chain.
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3. Adaptive Huber Regression on Markov-dependent Data.
PMID:日期:2019-09-25High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure - Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.
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4. MARKOV PROCESSES CONDITIONED ON THEIR LOCATION AT LARGE EXPONENTIAL TIMES.
PMID:日期:2018-06-14Suppose that ( ) is a one-dimensional Brownian motion with negative drift -. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like conditioned to hit 0, after which time it behaves as killed at the last time visits 0. Equivalently, the limit process has the dynamics of the killed "bang-bang" Brownian motion that evolves like Brownian motion with positive drift + when it is negative, like Brownian motion with negative drift - when it is positive, and is killed according to the local time spent at 0. An extension of this result holds in great generality for a Borel right process conditioned to be in some state at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the "bang-bang" construction for a general Markov process. As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the -transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.
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5. Heavy-tailed fractional Pearson diffusions.
PMID:日期:2017-03-18We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
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6. DOOB-MARTIN COMPACTIFICATION OF A MARKOV CHAIN FOR GROWING RANDOM WORDS SEQUENTIALLY.
PMID:日期:2016-12-05We consider a Markov chain that iteratively generates a sequence of random finite words in such a way that the word is uniformly distributed over the set of words of length 2 in which letters are and letters are at each step an and a are shuffled in uniformly at random among the letters of the current word. We obtain a concrete characterization of the Doob-Martin boundary of this Markov chain and thereby delineate all the ways in which the Markov chain can be conditioned to behave at large times. Writing for the number of letters (equivalently, ) in the finite word , we show that a sequence ( ) of finite words converges to a point in the boundary if, for an arbitrary word there is convergence as tends to infinity of the probability that the selection of () letters and () letters uniformly at random from and maintaining their relative order results in . We exhibit a bijective correspondence between the points in the boundary and ergodic random total orders on the set {, , , , …} that have distributions which are separately invariant under finite permutations of the indices of the 's and those of the 's. We establish a further bijective correspondence between the set of such random total orders and the set of pairs (, ) of diffuse probability measures on [0,1] such that ½( + ) is Lebesgue measure: the restriction of the random total order to {, ,…, } is obtained by taking ,…, (resp. ,… , ) i.i.d. with common distribution (resp. ), letting (,…, ) be {, ,…, , } in increasing order, and declaring that the smallest element in the restricted total order is (resp. ) if = (resp. = ).
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7. Asymptotic Normality of Quadratic Estimators.
PMID:日期:2016-12We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
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8. Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics.
PMID:日期:2016-12We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2012) concerning exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on "adjusted" inequalities of the type proved originally by Dvoretzky et al. (1956) and by Massart (1990) for one-sample versions of these statistics.
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9. A law of the iterated logarithm for Grenander's estimator.
PMID:日期:2016-04-29In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If () > 0, () 0, and is continuous in a neighborhood of , then [Formula: see text]almost surely where [Formula: see text]here [Formula: see text] is the two-sided Strassen limit set on [Formula: see text]. The proof relies on laws of the iterated logarithm for local empirical processes, Groeneboom's switching relation, and properties of Strassen's limit set analogous to distributional properties of Brownian motion.
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10. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.
PMID:日期:2014-05-30Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.