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

Haoyi Mo, Mengling Li, Feiqi Deng, Xuerong Mao

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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.
Original languageEnglish
JournalScience in China Series F - Information Sciences
DOIs
Publication statusAccepted/In press - 5 Dec 2017

Keywords

  • neutral stochastic functional differential equations with jumps
  • almost sure exponential stability
  • mean-square exponential stability
  • Euler-Maruyama method

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