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.

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.

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.

DOI : 10.1214/13-AIHP595
Classification : 60G51
Mots clés : regenerative set, subordinator, Bernstein function
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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. http://www.numdam.org/articles/10.1214/13-AIHP595/

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