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We provide a functional central limit theorem for a broad class of smooth functions for possibly noncausal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a…

Statistics Theory · Mathematics 2022-10-03 Carina Beering , Anne Leucht

In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the…

Machine Learning · Statistics 2025-10-15 Bogdan Butyrin , Eric Moulines , Alexey Naumov , Sergey Samsonov , Qi-Man Shao , Zhuo-Song Zhang

New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that…

Statistics Theory · Mathematics 2008-12-18 Michael H. Neumann , Efstathios Paparoditis

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

Networking and Internet Architecture · Computer Science 2011-06-22 Yang Zhang , Edwin K. P. Chong , Jan Hannig , Donald Estep

The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…

Computation · Statistics 2024-02-27 Charly Andral , Randal Douc , Hugo Marival , Christian P. Robert

In this paper we study the almost sure central limit theorem started from a point for additive functionals of a stationary and ergodic Markov chain via a martingale approximation in the almost sure sense. As a consequence we derive the…

Probability · Mathematics 2009-11-26 Christophe Cuny , Magda Peligrad

We prove a non-asymptotic central limit theorem for vector-valued martingale differences using Stein's method, and use Poisson's equation to extend the result to functions of Markov Chains. We then show that these results can be applied to…

Probability · Mathematics 2026-02-10 R. Srikant

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…

Probability · Mathematics 2010-07-14 Atul Mallik , Michael Woodroofe

Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions. In this paper, we study a general…

Statistics Theory · Mathematics 2011-07-15 Gersende Fort , Eric Moulines , Pierre Priouret , Pierre Vandekerkhove

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

Combinatorics · Mathematics 2024-09-25 Aaron Abrams , Eric Babson , Henry Landau , Zeph Landau , James Pommersheim

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…

Probability · Mathematics 2024-07-08 Zhishui Hua , Wei Wanga , Liang Dong

The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well known result with a long history. In this paper we present applications to two finite-memory versions of the Elephant Random Walk, solving a problem from…

Probability · Mathematics 2020-05-04 Iddo Ben-Ari , Jonah Green , Taylor Meredith , Hugo Panzo , Xiaoran Tan

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

Statistics Theory · Mathematics 2026-03-26 Ziwei Su , Imon Banerjee , Diego Klabjan

We propose and analyze a model-based bootstrap for transition kernels in finite controlled Markov chains (CMCs) with possibly nonstationary or history-dependent control policies, a setting that arises naturally in offline reinforcement…

Machine Learning · Statistics 2026-05-13 Ziwei Su , Imon Banerjee , Diego Klabjan

This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…

Statistical Mechanics · Physics 2007-05-23 D. Gabrielli , A. Galves , D. Guiol

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

Probability · Mathematics 2009-11-11 V. Shcherbakov

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…

Probability · Mathematics 2026-03-24 Ioan Scheffel , Marco Oesting , Gilles Stupfler

This article presents a bootstrap approximation to the Lp_statistics of kernel density estimator in length-biased model. Length-biased data arise in many situations, such as survival analysis, renewal processes and physics. The article…

Probability · Mathematics 2017-05-30 Raheleh Zamini

We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…

Probability · Mathematics 2025-11-18 Persi Diaconis , Brett Kolesnik

In this paper we give sufficient conditions for the almost sure central limit theorem started at a point, known under the name of quenched central limit theorem. This is achieved by using a new idea of conditioning with respect to both the…

Probability · Mathematics 2022-09-08 Magda Peligrad