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Binary Trees, Exploration Processes, and an Extended Ray-Knight Theorem

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  04 February 2016

Mamadou Ba ,
Etienne Pardoux  and
Ahmadou Bamba Sow
Mamadou Ba*
Affiliation:
Aix-Marseille Université
Etienne Pardoux*
Affiliation:
Aix-Marseille Université
Ahmadou Bamba Sow*
Affiliation:
Université Gaston Berger
*
∗ Postal address: Centre de Mathématiques et d'Informatique, LATP-CNRS, Aix-Marseille Université, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France.
∗ Postal address: Centre de Mathématiques et d'Informatique, LATP-CNRS, Aix-Marseille Université, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France.
∗∗∗ Postal address: LERSTAD, Université Gaston Berger, BP 234, Saint-Louis, Senegal. Email address: ahmadou-bamba.sow@ugb.edu.sn
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Abstract

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We study the bijection between binary Galton-Watson trees in continuous time and their exploration process, both in the subcritical and in the supercritical cases. We then take the limit over renormalized quantities, as the size of the population tends to ∞. We thus deduce Delmas' generalization of the second Ray-Knight theorem.

Keywords

Galton-Watson processFeller's branchingexploration processRay-Knight theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F17: Functional limit theorems; invariance principles
Secondary: 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 210 - 225
Copyright
© Applied Probability Trust 

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