Convergence and Stability of the Split-Step Theta Method for a Class of Stochastic Volterra Integro-Differential Equations Driven by Lévy Noise
Year: 2024
Author: Wei Zhang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1688–1713
Abstract
In this paper, we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations (SVIDEs) driven by Lévy noise. The existence, uniqueness, boundedness and mean square exponential stability of the analytic solutions for SVIDEs driven by Lévy noise are considered. The split-step theta method of SVIDEs driven by Lévy noise is proposed. The boundedness of the numerical solution and strong convergence are proved. Moreover, its mean square exponential stability is obtained. Some numerical examples are given to support the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2307-m2022-0194
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1688–1713
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Stochastic Volterra integro-differential equations Existence and uniqueness Stability Split-step theta method Convergence.
Author Details
Wei Zhang Email