Local limit theory and large deviations for supercritical Branching processes

Authors
Ney, Peter E. Vidyashankar, Anand N.
Citation
E. Ney, Peter et N. Vidyashankar, Anand, Local limit theory and large deviations for supercritical Branching processes, Annals of applied probability , 14(3), 2004, pp. 1135-1166
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
14
Issue
3
Year of publication
2004
Pages
1135 - 1166
Database
ACNP
SICI code
Abstract
In this paper we study several aspects of the growth of a supercritical Galton.Watson process {Zn:n.1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Zn, that is, the behavior of P(Zn=vn) as vn.., and use this to study conditional large deviations of {YZn:n.1}, where Yn satisfies an LDP, particularly of {Zn.1Zn+1:n.1} conditioned on Zn.vn.