Asymptotic laws for compositions derived from transformed subordinators
| dc.creator | Gnedin, Alexander | |
| dc.creator | Pitman, Jim | |
| dc.creator | Yor, Marc | |
| dc.date | 2004-03-25 | |
| dc.date | 2006-05-24 | |
| dc.date.accessioned | 2026-07-07T06:36:03Z | |
| dc.date.available | 2026-07-07T06:36:03Z | |
| dc.description | A 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.description | Published 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.identifier | https://arxiv.org/abs/math/0403438 | |
| dc.identifier | http://arxiv.org/abs/math/0403438 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 2, 468-492 | |
| dc.identifier | doi:10.1214/009117905000000639 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99971 | |
| dc.subject | Probability | |
| dc.subject | 60G09, 60C05 (Primary) | |
| dc.title | Asymptotic laws for compositions derived from transformed subordinators | |
| dc.type | text |