Numerical schemes for stochastic Volterra integral equations with weakly singular kernels

主讲人：黄乘明 华中科技大学教授

时间：2022年12月7日10：00

地点：腾讯会议 145 497 173

举办单位：数理学院

主讲人介绍：黄乘明，华中科技大学教授、博士生导师；兼任中国数学会计算数学分会常务理事；曾经和现任J Comput Appl Math、J Frankl Inst等4个SCI期刊编委。主要从事微分方程数值计算研究，主持国家自然科学基金项目7项，在SINUM、SISC、Numer Math、IMAJNA、JCP、JSC等学术期刊发表SCI论文100余篇。

内容介绍：In this talk we first establish the existence, uniqueness and Hölder continuity of the solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, with singularities α ∈ (0, 1) for the drift term and β ∈ (0, 1/2) for the stochastic term. Subsequently, we propose a θ-Euler–Maruyama scheme and a Milstein scheme to solve the equations numerically and obtain strong rates of convergence for both schemes in Lp norm for any p ≥1. For the θ-Euler–Maruyama scheme the rate is min{1−α, 1/2−β} and for the Milstein scheme is min{1−α, 1−2β}. These results on the rates of convergence are significantly different from those it is similar schemes for the SVIEs with regular kernels. This talk is based on the joint work with Dr. Min Li and Professor Yaozhong Hu.