STOCHASTIC METHODS FOR MULTIPLE INTEGRALS OVER UNBOUNDED REGIONS

Recent work in the development of stochastic methods for multiple inte grals over unbounded regions is reviewed and generalized. This include s randomization or deterministic rules, and new stochastic rules for i ntegrals with multivariate Normal weight. Stochastic spherical-radial rules are also discussed. These rules use a spherical-radial transform ation of the infinite integration region and combine stochastic rules for the infinite radial interval with stochastic rules for the spheric al surface. Example problems taken from Bayesian statistical analysis and computational finance are used to illustrate the use of the differ ent methods. (C) 1998 IMACS/Elsevier Science B.V.