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Mean-square stability of the Euler-Maruyama method for stochastic differential delay equations with jumps. (English) Zbl 1215.65016
The authors investigate the mean-square (MS) stability of the Euler-Maruyama method for stochastic differential delay equations (SDDEs) with jump, give the definition of the MS-stability of numerical methods for SDDEs with jumps, and a sufficient condition of the MS-stability of Euler-Maruyama methods for SDDEs with jumps. The presented numerical experiment verifies the theoretical results.
MSC:
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
34K60Qualitative investigation and simulation of models
34K28Numerical approximation of solutions of functional-differential equations
34F05ODE with randomness
60H35Computational methods for stochastic equations
65L20Stability and convergence of numerical methods for ODE