Year: 2021
Author: Guangjie Li, Qigui Yang
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 192–206
Abstract
In this paper, we investigate the stability of the split-step theta (SST) method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations (NSDDEs) with Markov switching and jumps. As we know, there are few results on the stability of numerical solutions for NSDDEs with Markov switching and jumps. The purpose of this paper is to enrich conclusions in such respect. It first devotes to showing that the trivial solution of the NSDDE with Markov switching and jumps is exponentially mean square stable and asymptotically mean square stable under some suitable conditions. If the drift coefficient also satisfies the linear growth condition, it then proves that the SST method applied to the NSDDE with Markov switching and jumps shares the same conclusions with the exact solution. Moreover, a numerical example is demonstrated to illustrate the obtained results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1910-m2019-0078
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 192–206
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Exponential mean-square stability Neutral stochastic delay differential equations Split-step theta method Markov switching and jumps.