TY - JOUR
T1 - Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations
AU - Zhang , Wei
JO - Journal of Computational Mathematics
VL - 4
SP - 607
EP - 623
PY - 2022
DA - 2022/04
SN - 40
DO - http://doi.org/10.4208/jcm.2101-m2020-0070
UR - https://global-sci.org/intro/article_detail/jcm/20503.html
KW - Strong convergence, Stochastic Volterra integral equations, Euler-Maruyama method, Lipschitz condition.
AB - <p style="text-align: justify;">In this paper, we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations (SVIEs). It is known that the strong convergence order of the Euler-Maruyama method is $\frac12$. However, the strong superconvergence order $1$ can be obtained for a class of SVIEs if the kernels $\sigma_{i}(t, t) = 0$ for $i=1$ and $2$; otherwise, the strong convergence order is $\frac12$. Moreover, the theoretical results are illustrated by some numerical examples.</p>