Probability Seminars——Long-term behaviors of stochastic flows of continuous-state branching processes and extremal processes
主 题: Probability Seminars——Long-term behaviors of stochastic flows of continuous-state branching processes and extremal processes
报告人: Prof. Chunhua Ma (Nankai University)
时 间: 2018-06-04 15:00-16:00
地 点: Room 1418, Sciences Building No. 1
Abstract: A class of stochastic flows of continuous state branching processes were constructed by Le Gall and Bertoin (2000) and Dawson and Li (2012) through subordinators and SDEs respectively. In this work, we study the long-term behaviors of flows of continuous-state branching processes through extremal processes, which arise in the case of supercritical processes with infinite mean and of subcritical processes with infinite variation. The jumps of these extremal processes are interpreted as specific initial individuals whose progenies overwhelm the population. These individuals, which correspond to the records of a certain Poisson point process embedded in the flow, are called super-individuals. They radically increase the growth rate to $+\infty$ in the supercritical case, and slow down the rate of extinction in the subcritical one.