Journal of Applied Probability

How did we get here?

Kais Hamza and Fima C. Klebaner

Abstract

Looking at a large branching population we determine along which path the population that started at 1 at time 0 ended up in B at time N. The result describes the density process, that is, population numbers divided by the initial number K (where K is assumed to be large). The model considered is that of a Galton-Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go down and then increase. This phenomenon requires further investigation. The technique uses large deviations, and the rate function based on Cramer's theorem is given. It also involves analysis of existence of solutions of a certain algebraic equation.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 63-72.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528467

Digital Object Identifier
doi:10.1239/jap/1417528467

Mathematical Reviews number (MathSciNet)
MR3317350

Zentralblatt MATH identifier
1310.60117

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations

Keywords
Branching process large deviations most likely path

Citation

Hamza, Kais; Klebaner, Fima C. How did we get here?. J. Appl. Probab. 51A (2014), 63--72. doi:10.1239/jap/1417528467. https://projecteuclid.org/euclid.jap/1417528467


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