The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels

Abstract

This paper focuses on the randomized Milstein scheme for approximating solutions to stochastic Volterra integral equations with weakly singular kernels and non-differentiable drift coefficients. An essential component of the error analysis involves the utilization of randomized quadrature rule for stochastic integral to avoid the Taylor expansion in the drift coefficient. Finally, we implement the simulation of multiple singular stochastic integral in the numerical experiment by applying the Riemann-Stieltjes integral.