A new variance-reduction technique for regenerative simulations of Markov chains

We propose a new estimator for some performance measures obtained from a regenerative simulation of a discrete-time Markov chain. Our new estimator is based on the idea of generating (uniform) random permutations of cycles corresponding to a certain state, and it has no larger (and typically smaller) mean squared error than the standard estimator. We show that our method can be used to derive a new estimator for the time-average variance parameter of a regenerative simulation.