Some limit theorems for subcritical branching processes in random environment
主 题: Some limit theorems for subcritical branching processes in random environment
报告人: Prof. V. Vatutin (Steklov Mathematical Institute, Moscow,Russia)
时 间: 2016-04-18 16:00 - 17:00
地 点: 理科一号楼 1303(概率论系列报告)
Let $Z_n$ be the number of individuals in a branching process evolving in the environment generated by i.i.d. probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming that $EX<\infty$ we study the probability of survival, prove Yaglom type limit theorems for the distribution of the number of particles in the process conditioned on its survival up to a distant moment n and describe the environments providing survival. The proofs use, in particular, a fine study of a random walk (with negative drift and heavy tails) conditioned to stay positive until time and to have a small positive value at time $n$, with $n\arrow\infty$ .