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 - <p style="text-align: justify;">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.</p>