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Elementary new proofs of classical limit theorems for Galton–Watson processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Jochen Geiger
Jochen Geiger*
Affiliation:
Universität Frankfurt
*
∗Postal address: Fachbereich Mathematik, Universität Frankfurt, Postfach 11 19 32, D-60054 Frankfurt am Main, Germany.
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Abstract

Classical results describe the asymptotic behaviour of a Galton–Watson branching process conditioned on non-extinction. We give new proofs of limit theorems in critical and subcritical cases. The proofs are based on the representation of conditioned Galton–Watson generation sizes as a sum of independent increments which is derived from the decomposition of the conditioned Galton–Watson family tree along the line of descent of the left-most particle.

Keywords

Galton–Watson treebranching processconditioned limit laws

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 301 - 309
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Research supported by Deutsche Forschungsgemeinschaft.

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