The usual form of local limit theorem is extended to an arbitrary supercritical Galton-Watson process with arbitrary initial distribution. The existence of a continuous density on $(0, \infty)$ for the limit random variable $W$, in the process initiated by a single ancestor, follows from the derivation.
Publié le : 1976-06-14
Classification:
Supercritical branching process,
general norming constants,
limit density,
local limit theorem,
subcritical analogue,
characteristic functions,
60J80,
60E05
@article{1176996100,
author = {Dubuc, S. and Seneta, E.},
title = {The Local Limit Theorem for the Galton-Watson Process},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 490-496},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996100}
}
Dubuc, S.; Seneta, E. The Local Limit Theorem for the Galton-Watson Process. Ann. Probab., Tome 4 (1976) no. 6, pp. 490-496. http://gdmltest.u-ga.fr/item/1176996100/