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Zbl 1215.65016
Tan, Jianguo; Wang, Hongli
Mean-square stability of the Euler-Maruyama method for stochastic differential delay equations with jumps. (English)
[J] Int. J. Comput. Math. 88, No. 2, 421-429 (2011). ISSN 0020-7160; ISSN 1029-0265/e

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.
[Jialin Hong (Beijing)]

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
34K60 Applications of functional-differential equations
34K28 Numerical approximation of solutions of FDE
34F05 ODE with randomness
60H35 Computational methods for stochastic equations
65L20 Stability of numerical methods for ODE

Keywords: stochastic differential delay equations; Poisson jumps; Euler-Maruyama methods; mean-square stability; numerical experiment

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