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March 2005 Regenerative composition structures
Alexander Gnedin, Jim Pitman
Ann. Probab. 33(2): 445-479 (March 2005). DOI: 10.1214/009117904000000801

Abstract

A new class of random composition structures (the ordered analog of Kingman’s partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set. Examples are composition structures derived from residual allocation models, including one associated with the Ewens sampling formula, and composition structures derived from the zero set of a Brownian motion or Bessel process. We provide characterization results and formulas relating the distribution of the regenerative composition to the Lévy parameters of a subordinator whose range is the corresponding regenerative set. In particular, the only reversible regenerative composition structures are those associated with the interval partition of [0,1] generated by excursions of a standard Bessel bridge of dimension 2−2α for some α∈[0,1].

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Alexander Gnedin. Jim Pitman. "Regenerative composition structures." Ann. Probab. 33 (2) 445 - 479, March 2005. https://doi.org/10.1214/009117904000000801

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1070.60034
MathSciNet: MR2122798
Digital Object Identifier: 10.1214/009117904000000801

Subjects:
Primary: 60C05, 60G09

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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