School Seminars and Colloquia

Quasi-stationary distributions in biology

Stochastic Processes Seminar

by Professor Andrew Barbour

Institution: Universitaet Zuerich
Date: Thu 11th February 2010
Time: 3:15 PM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: The mathematical study of quasi-stationary distributions for 
random processes with certain extinction was originally stimulated
 by work of Ewens (1963) on diffusion processes in population
 genetics. Since then, a substantial body of theory has been
 developed, with many surprising discoveries: for instance, a 
single absorbing process may well have many different quasi-stationary
 distributions. The aim of this talk is to get back closer to the 
biological origins of the subject. In particular, a set of conditions 
is presented under which the quasi-equilibrium distribution is unique,
 and can easily be calculated: indeed, it is then close to the `return'
 distribution, as discussed by Ewens but frowned upon by some subsequent 

 (Joint work with P. K. Pollett)

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