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, 2024)
In this paper, we investigate the theoretical and numerical analysis of the stochasticVolterra integro-differential equations (SVIDEs) driven by Lévy noise. The existence,uniqueness, boundedness and mean square exponential stability of the analytic solutionsfor SVIDEs driven by Lévy noise are considered. The split-step theta method of SVIDEsdriven by Lévy noise is proposed. The boundedness of the numerical solution and strongconvergence are proved. Moreover, its mean square exponential stability is obtained. Somenumerical examples are given to support the theoretical results.