## Electronic Journal of Probability

### Asymptotic variance of stationary reversible and normal Markov processes

#### 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 $n$

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 20, 26 pp.

Dates
Accepted: 3 March 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067126

Digital Object Identifier
doi:10.1214/EJP.v20-3183

Mathematical Reviews number (MathSciNet)
MR3325090

Zentralblatt MATH identifier
1321.60070

Subjects
Primary: 60G10 60J05 30C85

Rights

#### Citation

Deligiannidis, George; Peligrad, Magda; Utev, Sergey. Asymptotic variance of stationary reversible and normal Markov processes. Electron. J. Probab. 20 (2015), paper no. 20, 26 pp. doi:10.1214/EJP.v20-3183. https://projecteuclid.org/euclid.ejp/1465067126

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