The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels
Year: 2025
Author: Zhaohang Wang, Zhuoqi Liu, Shuaibin Gao, Junhao Hu
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 540–564
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-299.220524
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 540–564
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Stochastic Volterra integral equation randomized Milstein scheme strong convergence randomized quadrature rule.