### STABILITY ANALYSIS OF THE SPLIT-STEP THETA METHOD FOR NONLINEAR REGIME-SWITCHING JUMP SYSTEMS

Guangjie Li1, Qigui Yang2

1. 1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510420, China;
2. Department of Mathematics, South China University of Technology, Guangzhou 510640, China
• Received:2019-03-25 Revised:2019-08-14 Published:2021-03-15
• Contact: Qigui Yang,Email:qgyang@scut.edu.cn
• Supported by:
The authors would like to thank anonymous referees and editors for their helpful comments and suggestions, which greatly improved the quality of this paper. This work is partially supported by the National Natural Science Foundation of China (Nos.11901398, 11671149, 11871225) and the Natural Science Foundation of Guangdong Province (No. 2017A03 0312006).

Guangjie Li, Qigui Yang. STABILITY ANALYSIS OF THE SPLIT-STEP THETA METHOD FOR NONLINEAR REGIME-SWITCHING JUMP SYSTEMS[J]. Journal of Computational Mathematics, 2021, 39(2): 192-206.

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 show 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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