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Weak convergence of delay SDEs with applications to Carathéodory approximation. (English) Zbl 1492.65027

Summary: In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H07 Stochastic calculus of variations and the Malliavin calculus
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