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

翻译：本文研究随机Milstein算法在近似求解含弱奇异核的随机Volterra积分方程中的应用，其中漂移系数不可微。误差分析的关键环节在于采用随机积分的随机化求积规则，从而避免对漂移系数函数进行泰勒展开。最后，在数值实验中通过应用黎曼-斯蒂尔杰斯积分实现了多重奇异随机积分的模拟。