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March 2006 Asymptotic laws for compositions derived from transformed subordinators
Alexander Gnedin, Jim Pitman, Marc Yor
Ann. Probab. 34(2): 468-492 (March 2006). DOI: 10.1214/009117905000000639


A random composition of n appears when the points of a random closed set ℛ̃⊂[0,1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts Kn of this composition and other related functionals under the assumption that ℛ̃=ϕ(S), where (St,t≥0) is a subordinator and ϕ:[0,∞]→[0,1] is a diffeomorphism. We derive the asymptotics of Kn when the Lévy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function ϕ(x)=1−ex, we establish a connection between the asymptotics of Kn and the exponential functional of the subordinator.


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Alexander Gnedin. Jim Pitman. Marc Yor. "Asymptotic laws for compositions derived from transformed subordinators." Ann. Probab. 34 (2) 468 - 492, March 2006.


Published: March 2006
First available in Project Euclid: 9 May 2006

zbMATH: 1142.60327
MathSciNet: MR2223948
Digital Object Identifier: 10.1214/009117905000000639

Primary: 60C05 , 60G09

Keywords: Composition structure , Regenerative set , regular variation , Sampling formulae

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 2 • March 2006
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