We develop an algorithm for simulating “perfect” random samples from the invariant measure of a Harris recurrent Markov chain.The method uses backward coupling of embedded regeneration times and works most effectively for stochastically monotone chains, where paths may be sandwiched between “upper” and “lower” processes. We give an approach to finding analytic bounds on the backward coupling times in the stochastically monotone case. An application to storage models is given.
"Perfect sampling of ergodic Harris chains." Ann. Appl. Probab. 11 (2) 438 - 451, May 2001. https://doi.org/10.1214/aoap/1015345299