Replication splitting and variance for simulating discrete-parameter stochastic processes

Abstract

Previous results for stationary continuous-time processes concerning allocation of a fixed amount of simulation effort across independent replications are extended both to stationary and certain non-stationary discrete-time processes. In particular, in the presence of positive autocorrelation, variance is reduced if more short replications are designed. The magnitude, however, of the variance reduction is not great as long as the computation budget is not tight, suggesting that a good strategy is to design for a moderate number of replications in any case, which also mitigates potential bias problems.