科研交流
您的位置>> 首 页 > 科研交流 > 学术交流 > 正文
学术交流

数学学院、所系列学术报告(763场):李增沪 教授

发表于: 2018-05-08 13:07  点击:

题目:Genealogical structures of a population with competition

报告人:李增沪 教授

时间:2018年5月9日9:00-10:00

地点:数学楼3楼会议室

报告人简介: 李增沪,北京师范大学数学科学学院院长,数学与复杂系统教育部重点实验室主任,国家杰出青年科学基金获得者,教育部长江学者特聘教授,Fellow of Institute of Mathematical Statistics (美国)。学术服务工作包括中国概率统计学会副理事长(2006-2014)、Bernoulli Society for Mathematical Statistics and Probability理事(2009-2013)、《De Gruyter Studies in Mathematics》丛书编委、《Acta Mathematica Sinica (English Series)》等刊物编委。多次应邀参加国际会议并做报告,其中包括本学科最重要的系列国际学术会议“随机过程及其应用国际会议”(第31届,2006年巴黎)上的1小时大会邀请报告。主要研究领域包括测度值马尔可夫过程、分枝马尔可夫过程、随机金融模型等。

摘要:A continuous-state branching process is the mathematical model for the random evolution 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 of continuous-state branching processes was constructed in Dawson and Li (2012) as strong solutions to a stochastic equation driven by space-time noises. By a simple variation of the stochastic equation, a more general population model can be constructed by introducing a competition structure through a function called 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 based on 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 models with or without competition. However, up to now the stochastic equation is established only for the model with a nontrivial diffusion component. This talk is based on a joint work with E. Pardoux (Aix-Marseille) and A. Wakolbinger (Frankfurt).