Volume 21, 2017
|Page(s)||1 - 33|
|Published online||27 February 2017|
Non-binary branching process and non-Markovian exploration process
1 Aix-Marseille Univ., CNRS, Centrale Marseille, I2M, Marseille, France.
2 LERSTAD, Université Gaston Berger, BP 234, Saint Louis, Sénégal.
Received: 2 December 2015
Revised: 6 October 2016
Accepted: 2 November 2016
We study both a continuous time non-binary Galton−Watson random tree and its exploration (or height) process in the subcritical, critical and supercritical cases. We then renormalize our branching process and exploration process, and take the weak limit as the size of the population tends to infinity.
Mathematics Subject Classification: 60J80 / 60J85 / 92D25
Key words: Branching process / exploration process / local time / weak limit
© EDP Sciences, SMAI, 2017
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