TY - JOUR
T1 - Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion
AU - Wang , Mengjie
AU - Dai , Xinjie
AU - Xiao , Aiguo
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 202
EP - 217
PY - 2021
DA - 2021/11
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0384
UR - https://global-sci.org/intro/article_detail/aamm/19982.html
KW - Stochastic Volterra integro-differential equations, Riemann--Liouville fractional Brownian motion, well-posedness, strong convergence.
AB - <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>