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On the invariance principle for reversible Markov chains
Published online by Cambridge University Press: 21 June 2016
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.
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- Copyright © Applied Probability Trust 2016
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