@Article{AAMM-14-1,
author = {Wang, Mengjie and Xinjie, Dai and Xiao, Aiguo},
title = {Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {1},
pages = {202--217},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0384},
url = {https://global-sci.com/article/72897/optimal-convergence-rate-of-theta-maruyama-method-for-stochastic-volterra-integro-differential-equations-with-riemann-liouville-fractional-brownian-motion}
}