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

Mo, Haoyi and Li, Mengling and Deng, Feiqi and Mao, Xuerong (2017) Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Science in China Series F - Information Sciences. ISSN 1009-2757 (In Press)

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    Abstract

    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.