SCIENCE CHINA Information Sciences, https://doi.org/10.1007/s11432-017-9301-y

Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

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  • ReceivedAug 8, 2017
  • AcceptedDec 4, 2017
  • PublishedDec 7, 2017


The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.

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This work was supported by the National Natural Science Foundation of China under Grants 61573156, 61503142, and the Key Youth Research Fund of Guangdong University of Technology under Grant 17ZK0010.

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