Conditions for the Applicability of the Regenerative Method

摘要

The regenerative method for estimating steady-state parameters is one of thebasic methods in the simulation literature. This method depends on central limit theorems for regenerative processes and weakly consistent estimates for the variance constants arising in the central limit theorem. A weak sufficient (and probably necessary) condition for both the central limit theorems and consistent estimates is given. Several references have claimed (without proof) strong consistency of the variance estimates under our condition. This claim seems to us unjustified and we hope this note helps clarify the situation. Also discussed is the relationship between conditions for the validity of the regenerative method and those for the validity of the standardized time series methods.