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 (2018) Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Science in China Series F - Information Sciences, 61 (7). 70214. ISSN 1009-2757 (https://doi.org/10.1007/s11432-017-9301-y)

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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.

ORCID iDs

Mo, Haoyi, Li, Mengling, Deng, Feiqi and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:62567
    Dates:
    Date
    Event
    4 June 2018
    Published
    5 December 2017
    Accepted
    8 August 2017
    Submitted
    Notes:© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Mo, H., Li, M., Deng, F. et al. Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Sci. China Inf. Sci. 61, 70214 (2018). https://doi.org/10.1007/s11432-017-9301-y
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:08 Dec 2017 10:15
    Last modified:11 Nov 2024 11:51
    URI:https://strathprints.strath.ac.uk/id/eprint/62567
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