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Comptes Rendus Mathématique
Volume 343, n° 3
pages 201-208 (août 2006)
Doi : 10.1016/j.crma.2006.06.010
Received : 24 Mars 2006 ;  accepted : 29 May 2006
Asymptotics for the distribution of lengths of excursions of a d -dimensional Bessel process  
Asymptotiques pour la distribution des longueurs des excursions dʼun processus de Bessel de dimension d ( )
 

Bernard Roynette a , Pierre Vallois a , Marc Yor b, c
a Université Henri-Poincaré, Institut Elie-Cartan, BP239, 54506 Vandoeuvre-les-Nancy cedex, France 
b Laboratoire de probabilités et modèles aléatoires, Universités Paris VI et VII, 4, place Jussieu, case 188, 75252 Paris cedex 05, France 
c Institut Universitaire de France, France 

Abstract

Let   denote a d -dimensional Bessel process  . For every  , we consider the times  , and  , as well as the three sequences:  ,  , and  , which consist of the lengths of excursions of R away from 0 before  , before t , and before  , respectively, each one being ranked by decreasing order.

We obtain a limit theorem concerning each of the laws of these three sequences, as  . The result is expressed in terms of a positive, -finite measure on the set   of decreasing sequences. is closely related with the Poisson-Dirichlet laws on  . To cite this article: B. Roynette et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Soit   un processus de Bessel de dimension  . Pour tout  , on considère les temps   et  , ainsi que les trois suites :  , resp.  , resp.   des longueurs dʼexcursions de R hors de 0, avant  , resp. avant t , resp. avant  , rangées par ordre décroissant.

Nous obtenons un théorème limite concernant chacune des lois de ces trois suites, lorsque  . Ce théorème sʼexprime à lʼaide dʼune mesure positive, -finie, sur  . est intimement liée aux lois de Poisson-Dirichlet sur  . Pour citer cet article : B. Roynette et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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