報(bào)告人：胡杉杉 博士

報(bào)告題目：Random dynamical systems for McKean-Vlasov SDEs via rough path theory

報(bào)告時(shí)間：2025年10月11日（周六）下午3：00

報(bào)告地點(diǎn)：云龍校區(qū)6號樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡介：

胡杉杉，天津大學(xué)和柏林工業(yè)大學(xué)在讀博士生，師從王鳳雨教授和Benjamin Gess教授，主要研究方向?yàn)殡S機(jī)微分方程和隨機(jī)動(dòng)力系統(tǒng)，目前已在Annals of Applied Probability上發(fā)表論文。

報(bào)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.