On the functional CLT for stationary Markov chains started at a point

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Barrera, David¹  Peligrad, Costel¹  Peligrad, Magda¹ 

[1] Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45221 USA

关键词: Functional central limit theorem;    Quenched convergence;    Functions of Markov chains;    Martingale approximation;    Reversible Markov chains;   

DOI  :  10.1016/j.spa.2015.12.001

来源: Elsevier

【 摘 要 】

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 this type of asymptotic result. One of the theorems shows that if a Markov chain is stationary ergodic and reversible, this result holds for bounded additive functionals of the chain which have a martingale coboundary in L-1 representation. Our results are also well adapted for strongly mixing sequences providing for this case an alternative, shorter approach to some recent results in the literature. (C) 2016 Published by Elsevier B.V.

【 授权许可】

Free