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研究生短课
发布时间: 2016-08-31     08:38   【返回上一页】 发布人:$curArticle.author


课程名称:BRANCHING PROCESSES IN RANDOM ENVIRONMENT
报告人:Professor Vladimir Vatutin, Steklov Mathematical Institute (Moscow)
地点:后主楼1220
时间:9月6日下午2:30-5:30;
9月13日下午2:30-5:30;
9月20日下午2:30-5:30;
9月27日下午2:30-5:30;
          
摘要:The course consists of 6 lectures devoted to branching processes in random
environment. The lectures include the following themes:

Definition of branching processes in random environment (BPRE). Quenched and annealed approaches. Associated random walk. Classification of BPRE.

Prokhorov-Donsker invariance principle. Conditional Brownian motion: Brownian meander and Brownain excursion. Iglehart invariance principle.

Sparre-Anderson and Spitzer identities. Tauberian theorem. Distribution of the minimum and maximum of a driftless random walk. Renewal functions related with ladder epochs of random walks. Arcsine law. Properties of the prospective minima of a random walk. Changes of measures.

Probability of survival for the critical BPRE under the quenched and an-nealed approaches. Conditional limit theorems for the distribution of the number of particles in a critical BPRE.

Classification of subcritical BPRE. Probability of survival and conditional limit theorems for weakly, intermediately and strongly subcritical BPRE.

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数学学院随机数学中心
2016-8-30