The Markov chain simulation method has been successfully used in many problems, including some that arise in Bayesian statistics. We give a self-contained proof of the convergence of this method in general state spaces under conditions that are easy to verify.
"On the convergence of the Markov chain simulation method." Ann. Statist. 24 (1) 69 - 100, February 1996. https://doi.org/10.1214/aos/1033066200