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

David Barrera, Costel Peligrad and Magda Peligrad

Stochastic Processes and their Applications, 2016, vol. 126, issue 7, 1885-1900

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.

Keywords: Functional central limit theorem; Quenched convergence; Functions of Markov chains; Martingale approximation; Reversible Markov chains (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.12.001

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