Open Access
November 2007 Regenerative real trees
Mathilde Weill
Ann. Probab. 35(6): 2091-2121 (November 2007). DOI: 10.1214/009117907000000187


In this work, we give a description of all σ-finite measures on the space of rooted compact ℝ-trees which satisfy a certain regenerative property. We show that any infinite measure which satisfies the regenerative property is the “law” of a Lévy tree, that is, the “law” of a tree-valued random variable that describes the genealogy of a population evolving according to a continuous-state branching process. On the other hand, we prove that a probability measure with the regenerative property must be the law of the genealogical tree associated with a continuous-time discrete-state branching process.


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Mathilde Weill. "Regenerative real trees." Ann. Probab. 35 (6) 2091 - 2121, November 2007.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1203.60134
MathSciNet: MR2353384
Digital Object Identifier: 10.1214/009117907000000187

Primary: 60J80

Keywords: branching processes , Galton–Watson trees , Lévy trees

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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