Consistent Markov branching trees with discrete edge lengths
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.
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Pages: 1-14
Publication Date: August 31, 2013
DOI: 10.1214/ECP.v18-2872
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