On the invariance principle for reversible Markov chains. (21st June 2016)

• Record Type: Journal Article
• Authors: Peligrad, Magda; Utev, Sergey
• Is Part Of: Journal of applied probability. Volume 53:Number 2(2016)
• Page Start: 593
• Page End: 599
• Publication Date: 2016-06-21
• Subjects: Reversible process, -- Markov chain, -- functional central limit theorem; Primary 60F05, -- 60F17, -- 60J05; 519.2
• DOI: 10.1017/jpr.2016.23
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.