The randomized Milstein scheme for stochastic Volterra integral equations with weakly singular kernels
Numerical Analysis
2023-12-07 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2312.03474,
title = {The randomized Milstein scheme for stochastic Volterra integral equations with weakly singular kernels},
author = {Zhaohang Wang and Zhuoqi Liu and Shuaibin Gao and Junhao Hu},
journal= {arXiv preprint arXiv:2312.03474},
year = {2023}
}