Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients

Abstract

We present Runge-Kutta methods of high accuracy for stochastic differential equations with constant diffusion coefficients. We analyze L2 convergence of these methods and present convergence proofs. For scalar equations a second-order method is derived, and for systems a method of order one-and-one-half is derived. We further consider a variance reduction technique based on Hermite expansions for evaluating expectations of functions of sample solutions. Numerical examples in two dimensions are presented.

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Cite this paper

@inproceedings{Chang2010NumericalSO, title={Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients}, author={Chien-Cheng Chang}, year={2010} }