Asymptotic variance of stationary reversible and normal Markov processes
  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 $n$. 
George Deligiannidis, Magda Peligrad and Sergey Utev
math.PR