The Annals of Probability

The Local Limit Theorem for the Galton-Watson Process

S. Dubuc and E. Seneta

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60E05: Distributions: general theory

Keywords
Supercritical branching process general norming constants limit density local limit theorem subcritical analogue characteristic functions

Citation

Dubuc, S.; Seneta, E. The Local Limit Theorem for the Galton-Watson Process. Ann. Probab. 4 (1976), no. 3, 490--496. doi:10.1214/aop/1176996100. https://projecteuclid.org/euclid.aop/1176996100


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