TY - JOUR
T1 - Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay
AU - Qi , Siyuan
AU - Lan , Guangqiang
JO - Journal of Computational Mathematics
VL - 3
SP - 437
EP - 452
PY - 2022
DA - 2022/02
SN - 40
DO - http://doi.org/10.4208/jcm.2010-m2020-0129
UR - https://global-sci.org/intro/article_detail/jcm/20245.html
KW - Stochastic Volterra integral equation, Euler-Maruyama method, Strong convergence, Time-dependent delay.
AB - <p style="text-align: justify;">We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper. Strong convergence rate (at fixed point) of the corresponding Euler-Maruyama method is obtained when coefficients $f$ and $g$ both satisfy local Lipschitz and linear growth conditions. An example is provided to interpret our conclusions. Our result generalizes and improves the conclusion in [J. Gao, H. Liang, S. Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348 (2019) 385-398.]</p>