Large deviations for i.i.d. replications of the total progeny of a Galton–Watson process

Autor:	Claudio Macci, Barbara Pacchiarotti
Jazyk:	angličtina
Rok vydání:	2017
Předmět:	Cramér’s theorem initial random population estimators of offspring mean Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Zdroj:	Modern Stochastics: Theory and Applications, Vol 4, Iss 1, Pp 1-13 (2017)
Druh dokumentu:	article
ISSN:	2351-6046 2351-6054
DOI:	10.15559/16-VMSTA72
Popis:	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 Cramér’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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/25c94c7cbdab41a6bd75a571cb7ce09b Zobrazit plný text záznamu View record in DOAJ