报告人：He Hui 教授（Beijing Normal University）

时间：2024年12月13日 10:00-

腾讯会议ID：900-545-714  

会议链接：https://meeting.tencent.com/dm/e7H6rMCCeCd6 

摘要：We consider a Feller diffusion (Zs,s≥0) (with diffusion coefficient√2and drift θ =0) that we condition on {Zt = at},where at is a deterministic function, and we study the limit in distribution of the conditioned process and of its genealogical tree as t → +∞.When at does not increase too rapidly, we obtain the standard size-biased process (and the associated genealogical tree given by the Kesten’s tree). When at behaves as αt2,we obtain a new process whose distribution is described by a Girsanov transformation and equivalently by a SDE with a Poissonian immigration (depending on α). Its associated genealogical tree is described by an infinite discrete skeleton (which does not satisfy the branching property) decorated with Brownian continuum random trees given by a Poisson point measure. At last if the time is permitted, we shall show how to recover above results from a Gibbs’viewpoint. This talk is based on joint works with Romain Abraham, Jean-Fran¸cois Delmas and Meltem Unel.

邀请人: 周国立

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