Almost Sure Exponential Stability of Numerical Solutions for Stochastic Pantograph Differential Equations with Poisson Jumps

Autor:	Amr Abou-Senna, Boping Tian
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	stochastic pantograph differential equation with jumps Poisson process Euler–Maruyama method backward Euler–Maruyama method almost sure exponential stability Lipschitz condition polynomial growth condition Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 17, p 3137 (2022)
Druh dokumentu:	article
ISSN:	10173137 2227-7390 28880943
DOI:	10.3390/math10173137
Popis:	The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations. This paper deals with the almost sure exponential stability of numerical solutions for stochastic pantograph differential equations interspersed with the Poisson jumps by using the discrete semimartingale convergence theorem. It is shown that the Euler–Maruyama method can reproduce the almost sure exponential stability under the linear growth condition. It is also shown that the backward Euler method can reproduce the almost sure exponential stability of the exact solution under the polynomial growth condition and the one-sided Lipschitz condition. Additionally, numerical examples are performed to validate our theoretical result.
Databáze:	Directory of Open Access Journals
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