On the functional CLT for stationary Markov Chains started at a point
arXiv:1503.05532
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.
Dedicated to the memory of Mikhail Gordin, 20 pages The paper will appear in Stochastic Processes and Their Applications
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