TY - JOUR
T1 - Stability Analysis of the Split-Step Theta Method for Nonlinear Regime-Switching Jump Systems
AU - Li , Guangjie
AU - Yang , Qigui
JO - Journal of Computational Mathematics
VL - 2
SP - 192
EP - 206
PY - 2020
DA - 2020/11
SN - 39
DO - http://doi.org/10.4208/jcm.1910-m2019-0078
UR - https://global-sci.org/intro/article_detail/jcm/18371.html
KW - Exponential mean-square stability, Neutral stochastic delay differential equations, Split-step theta method, Markov switching and jumps.
AB - <p style="text-align: justify;">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.</p>