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: https://orcid.org/0000-0002-6768-9864;-
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Item type: Article ID code: 62567 Dates: DateEvent4 June 2018Published5 December 2017Accepted8 August 2017SubmittedNotes: © 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: 21 Nov 2024 01:14 URI: https://strathprints.strath.ac.uk/id/eprint/62567