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A strong law and a central limit theorem for controlled Galton-Watson processes

Part of: Markov processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Daniel Pierre Loti Viaud
Daniel Pierre Loti Viaud*
Affiliation:
Université Paris VI
*
∗ Postal address: L.S.T.A., T.45–55, E.3, Boite 158, Université Paris VI, 4, place Jussieu, 75252 Paris Cedex 05, France.
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Abstract

Through the study of a simple embedded martingale we obtain an extension of the Kesten–Stigum theorem and prove a central limit theorem for controlled Galton-Watson processes.

Keywords

POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSKESTEN–STIGUM THEOREMMARTINGALE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G42: Martingales with discrete parameter 60F15: Strong theorems 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 22 - 37
Copyright
Copyright © Applied Probability Trust 1994 

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