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

Davood Ahmadian, Omid Farkhondeh Rouz
2020 Journal of Inequalities and Applications  
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
more » ... herit 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.
doi:10.1186/s13660-020-02452-3 fatcat:prlybru4grfzzp6y7dk42nmkgm