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Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching. (English) Zbl 1120.65003
Authors’ summary: The main purpose of this paper is to study the convergence of numerical solutions to a class of stochastic delay differential equations with Poisson jump and Markovian switching. A numerical approximation scheme is proposed to approximate the solution to stochastic delay differential equations with Poisson jump and Markovian switching. It is proved that the Euler approximation solution converge to the analytic solution in probability under weaker conditions. Some known results are generalized and improved. An example is provided to illustrate our theory.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
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