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Numerical solutions of stochastic functional differential equations

Mao, X. (2003) Numerical solutions of stochastic functional differential equations. LMS Journal of Computation and Mathematics, 6. pp. 141-161. ISSN 1461-1570

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Abstract

In this paper, the strong mean square convergence theory is established for the numerical solutions of stochastic functional differential equations (SFDEs) under the local Lipschitz condition and the linear growth condition. These two conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here were obtained under quite general conditions.