On the invariance principle for reversible Markov chains
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Publication:6406288
DOI10.1017/JPR.2016.23arXiv2207.13758MaRDI QIDQ6406288
Publication date: 27 July 2022
Abstract: In this paper, we investigate the functional central limit theorem 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 central limit theorem 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.
Central limit and other weak theorems (60F05) Discrete-time Markov processes on general state spaces (60J05) Functional limit theorems; invariance principles (60F17)
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