报告人：甘四清（中南大学）
报告时间：2026年5月10日（星期六）10:30-12:00
报告地点：科技楼南楼706室
报告摘要：In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong convergence of order one under globally Lipschitz coefficients. Nevertheless, many MV-SDEs arising from applications possess super-linearly growing drift and diffusion terms, where classical methods may diverge and particle corruption can occur. In the present work, we aim to fill this gap by developing a unified class of Milstein-type discretizations handling both super-linear drift and diffusion coefficients. The proposed framework includes the tamed-, tanh-, and sine-Milstein methods as special cases and establishes order-one strong convergence for the associated interacting particle system under mild regularity assumptions, requiring only once differentiable coefficients. In particular, our results complement Chen et al. (Electron. J. Probab., 2025), where a taming-based Euler scheme was only tested numerically without theoretical guarantees, by providing a rigorous convergence theory within a broader Milstein-type framework. The analysis relies on discrete-time arguments and binomial-type expansions, avoiding the continuous-time Itˆo approach that is standard in the literature. Numerical experiments are presented to illustrate the convergence behavior and support the theoretical findings.
报告人简介：甘四清，博士，中南大学教授，博士生导师，2001年毕业于中国科学院数学研究所，获理学博士学位，2001-2003年在清华大学计算机科学与技术系高性能计算研究所做博士后，曾先后访问美国、新加坡、香港等国内外名校。主要研究方向为确定性微分方程和随机微分方程数值解法。主持国家自然科学基金面上项目5项， 参加国家自然科学基金重大研究计划集成项目1项。在《SIAM J. Sci. Comput.》、 《BIT》、《Appl. Numer. Math.》、《J. Math. Anal. Appl.》、《中国科学》等国内外学术刊物上发表论文100余篇。2005年入选湖南省首批新世纪121人才工程。2014年湖南省优秀博士学位论文指导老师。
邀请人：黄乘明
