## The Annals of Probability

### The Local Limit Theorem for the Galton-Watson Process

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 490-496.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996100

Digital Object Identifier
doi:10.1214/aop/1176996100

Mathematical Reviews number (MathSciNet)
MR405610

Zentralblatt MATH identifier
0332.60059

JSTOR