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

Autor:	Davood Ahmadian, Omid Farkhondeh Rouz
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Split-step θ-Milstein scheme Exponential mean-square stability Stochastic delay integro-differential equations Poisson jump Lyapunov function Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-33 (2020)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-020-02452-3
Popis:	Abstract 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.
Databáze:	Directory of Open Access Journals
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