A class of special subordinators with nested ranges

Marchal, P.

doi:10.1214/13-AIHP595

Marchal, P.

Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 2, pp. 533-544.

Résumé
Abstract

Nous construisons, sur un unique espace de probabilités, une famille d’ensembles régénératifs $ℛ^{(α)}$ , indexée par toutes les fonctions mesurables $α : [0, 1] \to [0, 1]$ . Pour une fonction donnée $α$ , l’ensemble $ℛ^{(α)}$ a même loi que l’image d’un subordinateur spécial. Les fonctions constantes correspondent aux subordinateurs stables. Si $α \leq β$ , on a $ℛ^{(α)} \subset ℛ^{(β)}$ . D’autres exemples de subordinateurs spéciaux sont donnés dans le cas discret.

We construct, on a single probability space, a class of regenerative sets $ℛ^{(α)}$ , indexed by all measurable functions $α : [0, 1] \to [0, 1]$ . For each function $α$ , $ℛ^{(α)}$ , has the law of the range of a special subordinator. Constant functions correspond to stable subordinators. If $α \leq β$ , then $ℛ^{(α)} \subset ℛ^{(β)}$ . Other examples of special subordinators are given in the lattice case.

MR Zbl

DOI : 10.1214/13-AIHP595

Classification : 60G51
Mots-clés : regenerative set, subordinator, Bernstein function

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     title = {A class of special subordinators with nested ranges},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {533--544},
     publisher = {Gauthier-Villars},
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Marchal, P. A class of special subordinators with nested ranges. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 2, pp. 533-544. doi : 10.1214/13-AIHP595. https://www.numdam.org/articles/10.1214/13-AIHP595/

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