Genealogical structures of a population with competition


主题:   Genealogical structures of a population with competition主讲人:   李增沪地点:   松江校区2号学院楼331理学院报告厅时间:   2018-05-20 15:00:00组织单位:   理学院数学系


内容摘要:Acontinuous-state branching process is the mathematical model for the randomevolution of a large population. The genealogical structure the population is represented by a Levy forest, which is uniquely characterized by its height process. The later was constructed by Le Gall and Le Jan (1998) and Duquesne and Le Gall(2002) as a functional of a spectrally positive Levy process. A flow ofcontinuous-state branching processes was constructed in Dawson and Li (2012) asstrong solutions to a stochastic equation driven by space-time noises. By asimple variation of the stochastic equation, a more general population modelcan be constructed by introducing a competition structure through a functioncalled the competition mechanism. For a diffusion model with logistic computation, the genealogical structures were characterized by Le et al. (2013)and Pardoux and Wakolbinger (2011) in terms of a stochastic equation of the corresponding height process. The genealogical forest of the general model with competition was constructed in the recent work of Berestycki et al. (2017+) by pruning the Levy forest according to an intensity identified as a fixed point of certain transformation on the space of all adapted intensities determined by the competition mechanism. In this talk, we present a construction of the corresponding height process in terms of a stochastic integral equation basedon a Poisson point measure. This generalizes the results of Le et al. (2013)and Pardoux and Wakolbinger (2011) to general branching mechanisms. The advantage of this construction is that it unifies the treatments for modelswith or without competition. However, up to now the stochastic equation is established only for the model with a nontrivial diffusion component. This talkis based on a joint work with E. Pardoux (Aix-Marseille) and A. Wakolbinger(Frankfurt).

报告主持:闫理坦 教授

视频:   摄影: 撰写:闫理坦  信息员:唐晓亮  编辑:孙庆华