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2013 Consistent Markov branching trees with discrete edge lengths
Harry Crane
Author Affiliations +
Electron. Commun. Probab. 18: 1-14 (2013). DOI: 10.1214/ECP.v18-2872

Abstract

We study consistent collections of random fragmentation trees with random integer-valued edge lengths. We prove several equivalent necessary and sufficient conditions under which Geometrically distributed edge lengths can be consistently assigned to a Markov branching tree. Among these conditions is a characterization by a unique probability measure, which plays a role similar to the dislocation measure for homogeneous fragmentation processes. We discuss this and other connections to previous work on Markov branching trees and homogeneous fragmentation processes.

Citation

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Harry Crane. "Consistent Markov branching trees with discrete edge lengths." Electron. Commun. Probab. 18 1 - 14, 2013. https://doi.org/10.1214/ECP.v18-2872

Information

Accepted: 31 August 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1306.60126
MathSciNet: MR3101638
Digital Object Identifier: 10.1214/ECP.v18-2872

Subjects:
Primary: 60J80
Secondary: 60C05, 60G09

JOURNAL ARTICLE
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