Asymptotic variance of stationary reversible and normal Markov processes

George Deligiannidis; Magda Peligrad; Sergey Utev

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arXiv · 1405.2411

Asymptotic variance of stationary reversible and normal Markov processes

George Deligiannidis·Magda Peligrad·Sergey Utev

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Abstract

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class of Metropolis-Hastings algorithms which satisfy a central limit theorem and invariance principle when the variance is not linear in $n$.

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George Deligiannidis, Magda Peligrad, Sergey Utev. 2014-05-10. Asymptotic variance of stationary reversible and normal Markov processes. https://arxiv.org/abs/1405.2411

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