Path to extinction
by Professor Fima Klebaner
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