An introduction to numerical methods for stochastic differential equations. (English) Zbl 0942.65004

Acta Numerica 8, 197-246 (1999).
The author gives an overview and summary of discrete time strong and weak approximation techniques for the approximation of ordinary stochastic differential equations (SDEs). The numerical methods presented originate from stochastic counterparts to deterministic Taylor expansions of the strong solution of SDEs, now known as Wagner-Platen formula. The paper is written as an continuation of P.E. Kloeden and E. Platen [Numerical solution of stochastic differential equations. Applications of Mathematics. 23. Berlin: Springer-Verlag. 632 p. (1992; Zbl 0752.60043)], P.E. Kloeden, E. Platen and H. Schurz [Numerical solution of SDEs through computer experiments. Universitext. Berlin: Springer-Verlag. 292 p. (1994; Zbl 0789.65100)], G.N. Milstein [Numerical integration of stochastic differential equations, Mathematics and its Applications (Dordrecht). 313 p. Dordrecht: Kluwer Academic Publishers (1995; Zbl 0810.65144)] and D. Talay [Simulation of stochastic differential systems, in Kree, Paul and Wedig, Walter (ed.), Probabilistic methods in applied physics. Berlin: Springer-Verlag. Lect. Notes Phys. 451, 54-96 (1995; Zbl 0837.65150)]. This survey is supplemented by an extended literature list, partially updated till 1998.
For the entire collection see [Zbl 0921.00012].


65C30 Numerical solutions to stochastic differential and integral equations
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)