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Mathematics & Statistics

Colloquia — Fall 2005

Wednesday, November 23, 2005

Title
Speaker

Time
Place

Quasi-stationarity and exit times for a size-dependent branching process
Göran Högnäs
Finland
3:00pm-4:00pm
PHY 118
Arunava Mukherjea

Abstract

A size-dependent branching model of the evolution of a single species population is introduced. The short-term behavior mimics the corresponding deterministic dynamical system very closely, but the branching model hits $$0$$ eventually, i.e., the population goes extinct in contrast with the deterministic model which remains positive at all times. It turns out that the so-called quasi-stationary distribution (q.s.d.) of the branching model gives the right asymptotics. The q.s.d. approximates the attracting limit cycles of the deterministic system. I will also discuss some results, mainly due to Klebaner and Liptser, on the order of magnitude of the extinction times.

Title
Speaker

Time
Place