The Annals of Probability

Asymptotic laws for compositions derived from transformed subordinators

Alexander Gnedin, Jim Pitman, and Marc Yor

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Abstract

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.

Article information

Source
Ann. Probab. Volume 34, Number 2 (2006), 468-492.

Dates
First available in Project Euclid: 9 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1147179979

Digital Object Identifier
doi:10.1214/009117905000000639

Mathematical Reviews number (MathSciNet)
MR2223948

Zentralblatt MATH identifier
1142.60327

Subjects
Primary: 60G09: Exchangeability 60C05: Combinatorial probability

Keywords
Composition structure regenerative set sampling formulae regular variation

Citation

Gnedin, Alexander; Pitman, Jim; Yor, Marc. Asymptotic laws for compositions derived from transformed subordinators. Ann. Probab. 34 (2006), no. 2, 468--492. doi:10.1214/009117905000000639. https://projecteuclid.org/euclid.aop/1147179979


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