Randomized Estimators for Time Integrals

P. W. Glynn

Technical Report, Mathematics Research Center, University of Wisconsin, Madison (1983)

Let {X(t): t≥0} be a real-valued stochastic process and set α = ∫ X(t) G(dt), where G is a (non-random) distribution func t ion. I f t hE support of G is large, standard Monte carlo technique s for estimating α are inefficient, since X must be simulated over the entire support o f G. To avoid this difficulty, randomization schemes are derived that require simulation of X over random subsets of the support of G. Large-sample behavior of randomized estimators is studied in detail. Some variance reduction techniques are also presented.d