The weak convergence of regenerative processes using some excursion path decompositions

Abstract : We consider regenerative processes with values in some Polish space. We define their \epsilon-big excursions as excursions e such that f(e)>\epsilon, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of \epsilon-big excursions and of their endpoints, for all \epsilon in a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of this sequence for this general condition to hold and discuss possible generalizations of our approach to processes that can be written as the concatenation of i.i.d. paths.
Type de document :
Pré-publication, Document de travail
22 pages. 2012
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00670811
Contributeur : Amaury Lambert <>
Soumis le : jeudi 16 février 2012 - 10:46:51
Dernière modification le : lundi 29 mai 2017 - 14:21:36

Identifiants

  • HAL Id : hal-00670811, version 1
  • ARXIV : 1202.2878

Collections

UPMC | PMA | INSMI | USPC

Citation

Amaury Lambert, Florian Simatos. The weak convergence of regenerative processes using some excursion path decompositions. 22 pages. 2012. <hal-00670811>

Partager

Métriques

Consultations de la notice

167