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Volume 42, Issue 6
Convergence and Stability of the Split-Step Theta Method for a Class of Stochastic Volterra Integro-Differential Equations Driven by Lévy Noise

Wei Zhang

DOI: 10.4208/jcm.2307-m2022-0194

J. Comp. Math., 42 (2024), pp. 1688-1713.

Published online: 2024-11

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  • 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.

  • Keywords

Stochastic Volterra integro-differential equations, Existence and uniqueness, Stability, Split-step theta method, Convergence.

  • AMS Subject Headings

65C30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-1688, author = {Zhang , Wei}, title = {Convergence and Stability of the Split-Step Theta Method for a Class of Stochastic Volterra Integro-Differential Equations Driven by Lévy Noise}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2307-m2022-0194}, url = {http://global-sci.org/intro/article_detail/jcm/23512.html} }
TY - JOUR T1 - Convergence and Stability of the Split-Step Theta Method for a Class of Stochastic Volterra Integro-Differential Equations Driven by Lévy Noise AU - Zhang , Wei JO - Journal of Computational Mathematics VL - 6 SP - 1688 EP - 1713 PY - 2024 DA - 2024/11 SN - 42 DO - http://doi.org/10.4208/jcm.2307-m2022-0194 UR - https://global-sci.org/intro/article_detail/jcm/23512.html KW - Stochastic Volterra integro-differential equations, Existence and uniqueness, Stability, Split-step theta method, Convergence. AB -

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.

Zhang , Wei. (2024). Convergence and Stability of the Split-Step Theta Method for a Class of Stochastic Volterra Integro-Differential Equations Driven by Lévy Noise. Journal of Computational Mathematics. 42 (6). 1688-1713. doi:10.4208/jcm.2307-m2022-0194
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