Markov chain Monte Carlo asymptotic variance (${\sigma }_K^2(\psi )$)

For a stationary chain, the asymptotic variance of the sample mean is ${\mathrm{Var}}_{\pi }\psi +2{\sum }_{k\ge 1}{\mathrm{Cov}}_{\pi }(\psi (X_0),\psi (X_k))$ when the series converges.