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Zbl 0979.65007
Higham, Desmond J.
An algorithmic introduction to numerical simulation of stochastic differential equations. (English)
[J] SIAM Rev. 43, No.3, 525-546 (2001). ISSN 0036-1445; ISSN 1095-7200/e

Summary: A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler's method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable; however, no knowledge of advanced probability theory or stochastic processes is assumed. The article is built around $10$ MATLAB programs, and the topics covered include stochastic integration, the Euler--Maruyama method, Milstein's method, strong and weak convergence, linear stability, and the stochastic chain rule.

MSC 2000:: *65C30 Stochastic differential and integral equations
60-04 Machine computation, programs (probability theory)
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE
60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations
34F05 ODE with randomness

Keywords: Euler-Maruyama method; MATLAB; Milstein method; Monte Carlo method; stochastic simulation; strong and weak convergence; stochastic differential equations; linear stability

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Zentralblatt MATH Berlin [Germany]