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Convergence of numerical solutions to stochastic differential delay equations with Poisson jump and Markovian switching. (English) Zbl 1128.65010

The authors tackle the question of approximating the solutions of such equations as mentioned in the title. A step size is chosen first, and a discrete Markov chain is simulated to account for the Markovian switching. Then an explicit Euler-Maruyama approximation scheme is set out. Strong convergence to the exact solution under local Lipschitz conditions is investigated.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

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