报告题目：Self-Interacting diffusions with aging

报告时间：2025-03-23   09:00-10:00

报 告 人：Prof.Nicolas Meunier  University of Evry (Paris Saclay)

报告地点：雷军科技楼六楼报告厅（601）

Abstract：We study the long term behavior of a class of Self-Interacting Diffusions on R, where the particle is attracted or repelled by its past trajectory, with aging and linear interactions with past positions. The novelty of this model is to introduce a weight depending on past trajectories through a memory kernel to describe the aging phenomenon. In a first step, we study the case where the memory kernel is general of convolution type. We observe three distinct asymptotic regimes when time becomes large depending on the data and the first moment of the integral kernel.  We then study a more realistic non-convolution model and prove a similar transition between the first two regimes. At last, we study the particular case of an exponential memory kernel which allows to construct an explicit solution. This is a joint work with R. Roux.