Asymptotic variance of stationary reversible and normal Markov processes

2014/05/10 by George Deligiannidis, Deligiannidis, George, Magda Peligrad +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1405.2411

arxiv created 2014/05/10 · arxiv updated 2014/05/13

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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