Large deviations analysis of extinction in branching models

Fima C. Klebaner*, Robert Liptser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)55-69
Number of pages15
JournalMathematical Population Studies
Volume15
Issue number1
DOIs
StatePublished - Jan 2008

Funding

FundersFunder number
Australian Research CouncilDP0451657

    Keywords

    • Cramer's theorem
    • Extinction
    • Galton-Watson process
    • Large deviations
    • Legendre transform

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