Numerical solution of stochastic differential equations with constant diffusion coefficients

Author:
Chien Cheng Chang

Journal:
Math. Comp. **49** (1987), 523-542

MSC:
Primary 65U05

DOI:
https://doi.org/10.1090/S0025-5718-1987-0906186-6

MathSciNet review:
906186

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Abstract: We present Runge-Kutta methods of high accuracy for stochastic differential equations with constant diffusion coefficients. We analyze ${L_2}$ 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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Article copyright:
© Copyright 1987
American Mathematical Society