Related papers: A new CLT for additive functionals of Markov chain…

In this paper we study the additive functionals of Markov chains via conditioning with respect to both past and future of the chain. We shall point out new sufficient projective conditions, which assure that the variance of partial sums of…

In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…

In this paper we consider stationary Markov chains with trivial two-sided tail sigma field, and prove that additive functionals satisfy the central limit theorem provided the variance of partial sums divided by n is bounded.

In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy…

Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…

We prove an invariance principle (functional central limit theorem) for a vector-valued additive functional of a Markov chain for almost every starting point with respect to an ergodic equilibrium distribution. The hypothesis is a moment…

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…

The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…

This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…

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…

In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases. The results are also new in the stationary…

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…

In this paper, we study the quenched central limit theorem for the discrete Fourier transform. We show that the Fourier transform of a stationary ergodic process, suitable centered and normalized, satisfies the quenched CLT conditioned by…

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…

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…

Suppose that X_n, n>=0 is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observanle. We say that the observable satisfies the central limit theorem (C.L.T.) if Y_n:=N^{-1/2}\sum_{n=0}^NV(X_n)…

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of…

We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally…