Journal of Applied Probability

How did we get here?

Kais Hamza and Fima C. Klebaner


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

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

First available in Project Euclid: 2 December 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Branching process large deviations most likely path


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

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