no. 2
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 ℛ (α) , indexée par toutes les fonctions mesurables α:[0,1]→[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≤β, on a ℛ (α) ⊂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]→[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≤β, then ℛ (α) ⊂ℛ (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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     title = {A class of special subordinators with nested ranges},
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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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