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Asymptotic variance of stationary reversible and normal Markov processes. (English) Zbl 1321.60070
Summary: 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 an invariance principle when the variance is not linear in \(n\).

MSC:
60G10 Stationary stochastic processes
60J05 Discrete-time Markov processes on general state spaces
60J25 Continuous-time Markov processes on general state spaces
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
65C40 Numerical analysis or methods applied to Markov chains
30C85 Capacity and harmonic measure in the complex plane
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