TY - JOUR
T1 - The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels
AU - Wang , Zhaohang
AU - Liu , Zhuoqi
AU - Gao , Shuaibin
AU - Hu , Junhao
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 540
EP - 564
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2023-299.220524
UR - https://global-sci.org/intro/article_detail/eajam/24155.html
KW - Stochastic Volterra integral equation, randomized Milstein scheme, strong convergence, randomized quadrature rule.
AB - <p style="text-align: justify;">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.</p>