Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations (Journal of Computational Mathematics, 2022)
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 $σ_{i}(t, t) = 0$ for $i=1$ and $2$; otherwise, the strong convergence order is $\frac12$. Moreover, the theoretical results are illustrated by some numerical examples.
Keywords: Strong convergence; Stochastic Volterra integral equations; Euler-Maruyama method; Lipschitz condition.