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A survey of numerical methods for stochastic differential equations. (English) Zbl 0701.60054
This paper is a survey on research papers devoted to methods for approximating the solution of Ito stochastic differential equations of the form \[ dX_ t=a(X_ t)dt+b(X_ t)dW_ t+\int_{U}c(X_ t,u)M(du,dt), \] where W is an m-dimensional Wiener process and M(du,dt) is a Poisson martingale measure. The main emphasis is on the case where the last term in the above equation (the jump component) is absent. The methods cited include truncated Taylor approximation methods and Runge- Kutta methods. Strong and weak convergence criteria and order of convergence are discussed and used to classify the methods presented. The paper concludes with some brief comments on important factors to consider when selecting and implementing a numerical method for the Ito equation.
Reviewer: M.D.Lax

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C99 Probabilistic methods, stochastic differential equations
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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