Journal of Applied Probability

Binary trees, exploration processes, and an extended Ray-Knight theorem

Mamadou Ba, Etienne Pardoux, and Ahmadou Bamba Sow

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 49, Number 1 (2012), 210-225.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216843

Digital Object Identifier
doi:10.1239/jap/1331216843

Mathematical Reviews number (MathSciNet)
MR2952891

Zentralblatt MATH identifier
1252.60086

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F17: Functional limit theorems; invariance principles
Secondary: 92D25: Population dynamics (general)

Keywords
Galton-Watson process Feller's branching exploration process Ray-Knight theorem

Citation

Ba, Mamadou; Pardoux, Etienne; Sow, Ahmadou Bamba. Binary trees, exploration processes, and an extended Ray-Knight theorem. J. Appl. Probab. 49 (2012), no. 1, 210--225. doi:10.1239/jap/1331216843. https://projecteuclid.org/euclid.jap/1331216843


Export citation