Some further results in the theory of Galton Watson processes are extended to the more general set up of a branching process with random environments. The random distribution function of the limit random variable in the supercritical case (Athreya and Karlin, Ann. Math. Statist., 40 (1969) 743-763) is investigated, and a zero-one law is established. It is shown that this random distribution function is w.p. 1. either absolutely continuous on $(0, \infty)$ with only a jump at the origin or w.p. 1. it is singular. A set of conditions is given under which the former case holds.
Publié le : 1974-06-14
Classification:
Branching process,
branching process with random environment,
random environment,
stationary ergodic process,
supercritical branching process,
60J85,
60J80
@article{1176996668,
author = {Kaplan, Norman},
title = {A Note on the Supercritical Branching Processes with Random Environments},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 509-514},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996668}
}
Kaplan, Norman. A Note on the Supercritical Branching Processes with Random Environments. Ann. Probab., Tome 2 (1974) no. 6, pp. 509-514. http://gdmltest.u-ga.fr/item/1176996668/