Consider the problem of estimating the mean of a strictly stationary stochastic process by Monte Carlo sampling for the case in which the process has autocorrelation functions {α’ℝs’ℝ,ℝαℝ<1,s=0,¸±1,...}. For n independent sample paths each of length t and each beginning in the steady state, the paper derives the optimal policy for choosing n and t that minimize computing cost subject to meeting a specified accuracy criterion. In particular, it identifies conditions under which the optimal policy (n*,t*) takes each of the forms: n*>1 and t*=1, n*=1 and t*>1, and n*>1 and t*>1. Results are presented in terms of α and ø, a relative cost ratio. Also, the paper extends the analysis to autocorrelation functions that are convex combinations of geometrically decreasing quantities.
