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Approximation of solutions of stochastic differential equations by discontinuous Galerkin methods. (English) Zbl 0868.60051

A discontinuous Galerkin method is used to approximate the generalized solution of a system of stochastic differential equations in the Stratonovich sense. Questions of uniqueness, mean-square convergence and error of approximation methods are considered, and the computation of the solution of a variational problem is discussed.
Reviewer: A.Dale (Durban)

MSC:

60H20 Stochastic integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
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References:

[1] Delfour, M. C. and F. Dubeau: Discontinuous polynomial approximation in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations. Math, of Comp. 47 (1986), 169 - 189. · Zbl 0633.65068 · doi:10.2307/2008088
[2] Gichman, 1. 1. and A. V. Skorochod: Stochastic Differential Equations. Berlin et al.: Springer-Verlag 1972.
[3] Ikeda, N. and S. Watanabe: Stochastic Differential Equations. Amsterdam: North- Holland 1989. · Zbl 0684.60040
[4] Kloeden, P. E. and E. Platen: Numerical Solution of Stochastic Differential Equations. Berlin et al.: Springer-Verlag 1992. 1994. · Zbl 0752.60043
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