Asymptotic laws for compositions derived from transformed subordinators

dc.creatorGnedin, Alexander
dc.creatorPitman, Jim
dc.creatorYor, Marc
dc.date2004-03-25
dc.date2006-05-24
dc.date.accessioned2026-07-07T06:36:03Z
dc.date.available2026-07-07T06:36:03Z
dc.descriptionA random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this composition and other related functionals under the assumption that $\widetilde{\mathcal{R}}=ϕ(S_{\bullet})$, where $(S_t,t\geq0)$ is a subordinator and $ϕ:[0,\infty]\to[0,1]$ is a diffeomorphism. We derive the asymptotics of $K_n$ when the Lévy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $ϕ(x)=1-e^{-x}$, we establish a connection between the asymptotics of $K_n$ and the exponential functional of the subordinator.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000639 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0403438
dc.identifierhttp://arxiv.org/abs/math/0403438
dc.identifierAnnals of Probability 2006, Vol. 34, No. 2, 468-492
dc.identifierdoi:10.1214/009117905000000639
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99971
dc.subjectProbability
dc.subject60G09, 60C05 (Primary)
dc.titleAsymptotic laws for compositions derived from transformed subordinators
dc.typetext

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