Exponential mean-square stability of numerical solutions for stochastic delay integro-differential equations with Poisson jump

Journal of inequalities and applications

article

Davood Ahmadian¹  Omid Farkhondeh Rouz¹ 

[1] Faculty of Mathematical Sciences, University of Tabriz

关键词: Split-step θ -Milstein scheme;    Exponential mean-square stability;    Stochastic delay integro-differential equations;    Poisson jump;    Lyapunov function;   

DOI  :  10.1186/s13660-020-02452-3

学科分类：电力

来源: SpringerOpen

【 摘 要 】

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 θ-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.

【 授权许可】

CC BY