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Taylor approximation of the solutions of stochastic differential delay equations with Poisson jump. (English) Zbl 1221.60084

Summary: We are concerned with the stochastic differential delay equations with Poisson jump (SDDEsPJ). As stochastic differential equations, most SDDEsPJ cannot be solved explicitly. Therefore, numerical solutions have become an important issue in the study of SDDEsPJ. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJ when the drift and diffusion coefficients are Taylor approximations.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
60J75 Jump processes (MSC2010)
65C30 Numerical solutions to stochastic differential and integral equations
65L03 Numerical methods for functional-differential equations
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References:

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