On the CLT of additive functionals of Markov chains

2020/02/28 by Magda Peligrad, Peligrad, Magda
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.2003.00085

12 pages

arxiv created 2020/05/17 · arxiv updated 2020/05/19

Abstract

In this paper we study the additive functionals of Markov chains via conditioning with respect to both past and future of the chain. We shall point out new sufficient projective conditions, which assure that the variance of partial sums of n consecutive random variables of a stationary Markov chain is linear in n. The paper also addresses the central limit theorem problem and is listing several open questions.

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