School Seminars and Colloquia

On the Path to Extinction

Stochastic Processes Seminar

by Professor Peter Jagers


Institution: Chalmers University of Technology
Date: Thu 5th March 2009
Time: 3:15 PM
Location: Russell Love Theatre, Richard Berry Bldg, Uni of Melbourne

Abstract: Populations can die in many ways. Arguably the most basic is extinction for intrinsic reasons, by stably insufficient, i.e. subcritical, reproduction. We 
consider (moderately) large, subcritical general branching processes, and ask what the time T to extinction is.

It turns out that T has two components, both carrying weight, a deterministic part, proportional to the logarithm of initial population size, and a random part, with an approximate Gumbel distribution.

Then we consider the path to extinction. How large will the population be at time uT, 0
(Joint work with Fima Klebaner and Serik Sagitov, published in the Proc Nat.
 Acad. of US (2007) and J. Appl. Prob. (2007)).

For More Information: Aihua Xia xia@ms.unimelb.edu.au