Accurate Evaluation of Stochastic Wiener Integrals with Applications to Scattering in Random Media and to Nonlinear Filtering

In 1973 A. J. Chorin [Math. Comp., 27 (1973), pp. 1-15] reported quadrature formulas for the approximation of a class of Wiener path integrals by n-fold ordinary integrals with an error O(n-2). Similar formulas are presented here for certain stochastic Wiener function space integrals in which n-fold integral approximations result in errors O(n-2) or O(n-3/2). Stochastic Wiener integrals arise in the physics of wave propagation in random media and in signal estimation problems in communication theory. The present formulas provide simple, accurate computational tools for these applications, among others. This point is illustrated by several examples in the paper.