The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

@article{Xiu2002TheWP,
title={The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations},
author={Dongbin Xiu and George Em Karniadakis},
journal={SIAM J. Scientific Computing},
year={2002},
volume={24},
pages={619-644}
}

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener’s 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… CONTINUE READING