The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Abstract. We present a new method for solving stochastic di®erential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Speci¯cally, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte-Carlo simulations for low dimensional stochastic inputs.