The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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We present a new method for solving stochastic differential equations based on Galerking projections and extensions of Wieners polynomial chaos. Specifically, 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.
- Statistics and Probability