A Martingale Approach to Regenerative Simulation

P. W. Glynn and D. L. Iglehart

Probability in the Engineering and Informational Sciences, Vol. 9, 123-131 (1995)

The standard regenerative method for estimating steady-state parameters is extended to permit cycles that begin and end in different states. This result is established using the Dynkin martingale and a related solution to Poisson's equation. We compare the variance constant that appears in the associated central limit theorem with that arising from cycles that begin and end in the same state. The standard regenerative method has a smaller variance constant than does the alternative.