Filomat 2022 Volume 36, Issue 19, Pages: 6713-6734
https://doi.org/10.2298/FIL2219713Z
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Strong convergence of the Euler-Maruyama method for the generalized stochastic Volterra integral equations driven by Lévy noise
Zhang Wei (School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang, China), weizhanghlj@163.com
Li Rui (Qingdao Harbour Vocational and Technical College, Qingdao, Shandong, China), 052807@qdgw.edu.cn
In this paper, the theoretical and numerical analysis of the stochastic
Volterra integral equations (SVIEs) driven by Lévy noise are considered. We
investigate the existence, uniqueness, boundedness and Hölder continuity of
the analytic solutions for SVIEs driven by Lévy noise. The Euler-Maruyama
method for SVIEs driven by Lévy noise is proposed. The boundedness of the
numerical solution is proved, and the strong convergence order is obtained.
Some numerical examples are given to support the theoretical results.
Keywords: Stochastic Volterra integral equations, Existence and uniqueness, Hölder continuity, Euler-Maruyama method, Strong convergence
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