Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion
Year: 2022
Author: Mengjie Wang, Xinjie Dai, Aiguo Xiao
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 202–217
Abstract
This paper mainly considers the optimal convergence analysis of the $\theta$--Maruyama method for stochastic Volterra integro-differential equations (SVIDEs) driven by Riemann--Liouville fractional Brownian motion under the global Lipschitz and linear growth conditions. Firstly, based on the contraction mapping principle, we prove the well-posedness of the analytical solutions of the SVIDEs. Secondly, we show that the $\theta$--Maruyama method for the SVIDEs can achieve strong first-order convergence. In particular, when the $\theta$--Maruyama method degenerates to the explicit Euler--Maruyama method, our result improves the conclusion that the convergence rate is $H+\frac{1}{2},$ $ H\in(0,\frac{1}{2})$ by Yang et al., J. Comput. Appl. Math., 383 (2021), 113156. Finally, the numerical experiment verifies our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0384
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 202–217
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Stochastic Volterra integro-differential equations Riemann--Liouville fractional Brownian motion well-posedness strong convergence.
Author Details
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