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June, 1976 The Local Limit Theorem for the Galton-Watson Process
S. Dubuc, E. Seneta
Ann. Probab. 4(3): 490-496 (June, 1976). DOI: 10.1214/aop/1176996100


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.


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S. Dubuc. E. Seneta. "The Local Limit Theorem for the Galton-Watson Process." Ann. Probab. 4 (3) 490 - 496, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0332.60059
MathSciNet: MR405610
Digital Object Identifier: 10.1214/aop/1176996100

Primary: 60J80
Secondary: 60E05

Keywords: characteristic functions , general norming constants , limit density , local limit theorem , subcritical analogue , supercritical branching process

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
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