Electronic Communications in Probability

A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem

Yan-Xia Ren, Renming Song, and Zhenyao Sun

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In this note we propose a two-spine decomposition of the critical Galton-Watson tree and use this decomposition to give a probabilistic proof of Yaglom’s theorem.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 42, 12 pp.

Received: 7 March 2018
Accepted: 17 June 2018
First available in Project Euclid: 25 July 2018

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Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems

Galton-Watson process Galton-Watson tree spine decomposition Yaglom’s theorem martingale change of measure

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Ren, Yan-Xia; Song, Renming; Sun, Zhenyao. A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem. Electron. Commun. Probab. 23 (2018), paper no. 42, 12 pp. doi:10.1214/18-ECP143. https://projecteuclid.org/euclid.ecp/1532505673

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