On the functional CLT for stationary Markov Chains started at a point
Abstract
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.
Cite
@article{arxiv.1503.05532,
title = {On the functional CLT for stationary Markov Chains started at a point},
author = {David Barrera and Costel Peligrad and Magda Peligrad},
journal= {arXiv preprint arXiv:1503.05532},
year = {2016}
}
Comments
Dedicated to the memory of Mikhail Gordin, 20 pages The paper will appear in Stochastic Processes and Their Applications