# Path to extinction

*by Professor Fima Klebaner *

*Institution:*Monash University

*Date: Tue 11th September 2007*

*Time: 1:15 PM*

*Location: Russel Love Theatre, Richard Berry Building, Uni of Melb*

*Abstract*: We consider the size of a branching population at the time uT, where 0 u 1 and T is the time of extinction. For example, for u equals 0.5, it gives us size half-way to extinction, and when u varies between 0 and 1 we recover the path to extinction. We give an approximation when the population starts with a large number of indivduals

x, and show that the population is of order x 1-u. This approximation is

not so precise just before extinction when u is close 1. For this case we consider random time T-a for small a, and give an approximation for this case. It is joint

work with P. Jagers and S. Sagitov, Chalmers, Sweden.

*For More Information:* Associate Professor Aihua Xia A.Xia@ms.unimelb.edu.au