学术海报

10月11日 胡杉杉博士学术报告(数学与统计学院)

发布者:张永伟发布时间:2025-10-09浏览次数:14


人:胡杉杉 博士

报告题目:Random dynamical systems for McKean-Vlasov SDEs via rough path theory

报告时间:20251011(周六)下午3:00

报告地点云龙校区6号楼304会议室

主办单位:数学与统计学院、数学研究院、科学技术研究院

报告人简介:

胡杉杉,天津大学和柏林工业大学在读博士生,师从王凤雨教授和Benjamin Gess教授,主要研究方向为随机微分方程和随机动力系统,目前已在Annals of Applied Probability上发表论文。

报告摘要:

The existence of random dynamical systems for McKean--Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying stochastic differential equation (SDE) as a dynamical system on the product space $\RR^d \times \mathcal{P}(\RR^d)$. The proof relies on two main ingredients: At the level of the SDE, a pathwise rough path-based solution theory for SDEs with time-dependent coefficients is implemented, while at the level of the PDE a well-posedness theory is developed, for measurable solutions and allowing for degenerate diffusion coefficients.

The results apply in particular to the so-called ensemble Kalman sampler (EKS), proving the existence of an associated RDS under some assumptions on the posterior, as well as to the Lagrangian formulation of the Landau equation with Maxwell molecules. As a by-product of the main results, the uniqueness of solutions to non-linear Fokker--Planck equations associated to the EKS is shown.