Large Deviations Analysis of Extinction in Branching Models

Fima Klebaner and Robert Liptser

Mathematical Population Studies, 2008, vol. 15, issue 1, 55-69

Abstract: Cramer's classical theorem is applied to obtain large deviations in branching processes. This is a new avenue for analysis of models in discrete and continuous time. For the Galton-Watson process a new formula for the rate function in terms of the Legendre transform of its offspring distribution is derived. Further analysis of the approximate path to extinction produces a new interesting formula.

Keywords: Cramer's theorem; extinction; Galton-Watson process; large deviations; Legendre transform (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1080/08898480701792477

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