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Volume 15, Issue 3
The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels

Zhaohang Wang, Zhuoqi Liu, Shuaibin Gao & Junhao Hu

East Asian J. Appl. Math., 15 (2025), pp. 540-564.

Published online: 2025-06

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  • 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.

  • AMS Subject Headings

65C30, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-15-540, author = {Wang , ZhaohangLiu , ZhuoqiGao , Shuaibin and Hu , Junhao}, title = {The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels}, journal = {East Asian Journal on Applied Mathematics}, year = {2025}, volume = {15}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-299.220524}, url = {http://global-sci.org/intro/article_detail/eajam/24155.html} }
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 -

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.

Wang , ZhaohangLiu , ZhuoqiGao , Shuaibin and Hu , Junhao. (2025). The Randomized Milstein Scheme for Stochastic Volterra Integral Equations with Weakly Singular Kernels. East Asian Journal on Applied Mathematics. 15 (3). 540-564. doi:10.4208/eajam.2023-299.220524
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