Regenerative Simulation

Abstract

Heuristically, a regenerative stochastic process has the characteristic property that there exists a sequence of random time points, referred to as regeneration points or regeneration times, at which the process probabilistically restarts. Typically, the times at which a regenerative process probabilistically starts afresh occur when the process returns to some fixed state. The essence of regeneration is that the evolution of the process between any two successive regeneration points is a probabilistic replica of the process between any other two successive regeneration points. In the presence of certain mild regularity conditions, the regenerative structure guarantees the existence of a limiting distribution (“steady state”) for the process provided that the expected time between regeneration points is finite. Moreover, the limiting distribution of a regenerative process is determined (as a ratio of expected values) by the behavior of the process between any pair of successive regeneration points. These results have important implications (discussed in Section 2.3) for the analysis of simulation output.