Poissonian ensembles of loops of one-dimensional diffusions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

Poissonian ensembles of loops of one-dimensional diffusions

Titus Lupu

Résumé

We study the analogue of Poissonian ensembles of Markov loops ("loop soups") in the setting of one-dimensional diffusions. First we give a detailed description of the corresponding intensity measure. Then we identify the law of the occupation field of the Poissonian ensembles of loops. Finally we explain how to sample this Poissonian ensembles using two-dimensional Markov processes. We also state and prove a Vervaat-like relation between bridges conditioned by the value of their minimum and excursion that holds for all the diffusion we consider and not just for the Brownian motion.
Fichier principal
Vignette du fichier
onedimloops.pdf (674.54 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00788901 , version 1 (15-02-2013)
hal-00788901 , version 2 (18-04-2013)
hal-00788901 , version 3 (11-01-2014)
hal-00788901 , version 4 (07-01-2019)

Identifiants

Citer

Titus Lupu. Poissonian ensembles of loops of one-dimensional diffusions. 2013. ⟨hal-00788901v1⟩
144 Consultations
406 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More