Author:
Ahmadian Davood,Farkhondeh Rouz Omid
Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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