北航数学论坛学术报告

--几何测度论与相关领域讨论班

Nonlinear stochastic differential equations and nonlinear partial differential equations

Raphaёl Roux 副教授

（巴黎索邦大学）

报告时间：14：00-15：00，2026-03-19（星期四）

报告地点：学院路校区新主楼207

内容简介：In this talk, I will give an insight to a deep link between parabolic partial differential equations and stochastic processes. In the classical case, a diffusion process being given, the evolution of its distribution can be described by a linear partial differential equation, allowing to give a probabilistic interpretation to a large class of PDEs.

In the case where the PDE is nonlinear, one can still interpret it from a probabilistic point of view, but this time the process will depend on its own distribution : for example, one obtain a diffusion process whose coefficients are allowed to depend on the mean position of the process. In order to analyze this process, one can make it linear again by taking a large numbers of interacting copies of the process, the idea being to approximate the distribution of the process by an empirical measures. In the limit of infinitely many particles, one then typically obtains convergence results to the initial nonlinear process, called propagation of chaos.

I will discuss several types of non linearity and explain what kind of random processes can be used to give a probabilistic representation of those equations.

报告人简介：报告人Raphaёl Roux，法国索邦大学概率、统计与建模实验室（LPSM）的副教授，研究方向主要包括随机偏微分方程，随机过程，随机粒子运动建模等。Raphaёl Roux副教授关于随机粒子运动过程研究及建模领域的文章多次发表在国际顶刊上，并多次在国际学术会议和短期学术交流活动中做受邀报告。

邀请人：梁湘玉