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Large deviations for i.i.d. replications of the total progeny of a Galton--Watson process by Macci, Claudio; Pacchiarotti, Barbara is a scholarly article available to read on EtoBox.

What is Large deviations for i.i.d. replications of the total progeny of a Galton--Watson process about?

The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this paper, we illustrate the relationship between these two distributions when we consider the large deviation rate function (provided by Cram\'{e}r's theorem) for empirical means of i.i.d. random variables. We also consider the case with a random initial population. In the final part, we present large deviation results for sequences of estimators of the offspring mean based on i.i.d. replications of total progeny.

Author

Macci, Claudio; Pacchiarotti, Barbara

Published

2017

Language

EN