Journal
JOURNAL OF INEQUALITIES AND APPLICATIONS
Volume 2020, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1186/s13660-020-02452-3
Keywords
Split-step theta-Milstein scheme; Exponential mean-square stability; Stochastic delay integro-differential equations; Poisson jump; Lyapunov function
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In this paper, we investigate the exponential mean-square stability for both the solution of n-dimensional stochastic delay integro-differential equations (SDIDEs) with Poisson jump, as well for the split-step theta-Milstein (SSTM) scheme implemented of the proposed model. First, by virtue of Lyapunov function and continuous semi-martingale convergence theorem, we prove that the considered model has the property of exponential mean-square stability. Moreover, it is shown that the SSTM scheme can inherit the exponential mean-square stability by using the delayed difference inequality established in the paper. Eventually, three numerical examples are provided to show the effectiveness of the theoretical results.
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