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One-step approximations for stochastic functional differential equations. (English) Zbl 1105.65005

For systems of Itô stochastic functional differential equations, the author proves a convergence theorem in which global error estimates for a one step mean-square method are derived from estimates on its local error. The result is applied to analysis of mean-square convergence for drift-implicit one-step schemes.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
34K50 Stochastic functional-differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

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