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On the invariance principle for reversible Markov chains

Published online by Cambridge University Press:  21 June 2016

Magda Peligrad*
Affiliation:
University of Cincinnati
Sergey Utev*
Affiliation:
University of Leicester
*
* Postal address: Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, OH 45221-0025, USA. Email address: [email protected]
** Postal address: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK. Email address: [email protected]

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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2016 

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