课程名称：BRANCHING PROCESSES IN RANDOM ENVIRONMENT
报告人：Professor Vladimir Vatutin, Steklov Mathematical Institute (Moscow)
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.