Local limit theory and large deviations for supercritical Branching processes

Ney, Peter E.; Vidyashankar, Anand N.

Ann. Appl. Probab., Tome 14 (2004) no. 1, p. 1135-1166 / Harvested from Project Euclid

Résumé

In this paper we study several aspects of the growth of a supercritical Galton–Watson process {Z_n:n≥1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Z_n, that is, the behavior of P(Z_n=v_n) as v_n↗∞, and use this to study conditional large deviations of {Y_{Z_n}:n≥1}, where Y_n satisfies an LDP, particularly of {Z_n⁻¹Z_n+1:n≥1} conditioned on Z_n≥v_n.

Publié le : 2004-08-14
Classification: Branching processes, large deviations, local limit theorems., 60J80, 60F10

@article{1089736280,
     author = {Ney, Peter E. and Vidyashankar, Anand N.},
     title = {Local limit theory and large deviations for supercritical Branching processes},
     journal = {Ann. Appl. Probab.},
     volume = {14},
     number = {1},
     year = {2004},
     pages = { 1135-1166},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1089736280}
}

Ney, Peter E.; Vidyashankar, Anand N. Local limit theory and large deviations for supercritical Branching processes. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp.  1135-1166. http://gdmltest.u-ga.fr/item/1089736280/