Title: PDE and stochastic PDE arising from individual-based models
Speaker: Louis Fan
Speaker Info: University of Wisconsin-Madison
Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws in complex systems. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.Date: Tuesday, May 15, 2018
In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in mathematical modeling. I will also present novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of certain population dynamics.