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

2015/03/18 by Barrera, David, Peligrad, Costel, Peligrad, Magda
#60G10 #60G42 #60J05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/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 L₁ 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.

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