A class of special subordinators with nested ranges
Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 2, p. 533-544

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

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

DOI : https://doi.org/10.1214/13-AIHP595
Classification:  60G51
Keywords: regenerative set, subordinator, Bernstein function
@article{AIHPB_2015__51_2_533_0,
     author = {Marchal, P.},
     title = {A class of special subordinators with nested ranges},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {2},
     year = {2015},
     pages = {533-544},
     doi = {10.1214/13-AIHP595},
     mrnumber = {3335014},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2015__51_2_533_0}
}
Marchal, P. A class of special subordinators with nested ranges. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 2, pp. 533-544. doi : 10.1214/13-AIHP595. http://www.numdam.org/item/AIHPB_2015__51_2_533_0/

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