## The Annals of Probability

### A Note on the Supercritical Branching Processes with Random Environments

Norman Kaplan

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 2, Number 3 (1974), 509-514.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996668

Digital Object Identifier
doi:10.1214/aop/1176996668

Mathematical Reviews number (MathSciNet)
MR356265

Zentralblatt MATH identifier
0293.60079

JSTOR