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The weak convergence of regenerative processes using some excursion path decompositions

Lambert, Amaury and Simatos, Florian The weak convergence of regenerative processes using some excursion path decompositions. (2014) Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 50 (2). 492-511. ISSN 0246-0203

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Official URL: http://doi.org/10.1214/12-AIHP531

Abstract

We consider regenerative processes with values in some general Polish space. We define their ε-big excursions as excursions e such that φ(e) > ε, where φ 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 ε-big excursions and of their endpoints, for all ε in a 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. motifs.

Item Type:Article
HAL Id:hal-01890571
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Université de Paris Diderot - Paris 7 (FRANCE)
Other partners > Université Pierre et Marie Curie, Paris 6 - UPMC (FRANCE)
Other partners > Eindhoven University of Technology - TU/e (NETHERLANDS)
Laboratory name:
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Deposited By: Florian Simatos
Deposited On:08 Oct 2018 15:17

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