Stability Analysis of the Split-Step Theta Method for Nonlinear Regime-Switching Jump Systems (Journal of Computational Mathematics, 2020)
In this paper, we investigate the stability of the split-step theta (SST) method fora class of nonlinear regime-switching jump systems–neutral stochastic delay differentialequations (NSDDEs) with Markov switching and jumps. As we know, there are few resultson 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 exponentiallymean 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 theSST method applied to the NSDDE with Markov switching and jumps shares the sameconclusions with the exact solution. Moreover, a numerical example is demonstrated toillustrate the obtained results.