A class of special subordinators with nested ranges

We construct, on a single probability space, a class of regenerative sets \mathcal{R}^{(\alpha)}, indexed by all measurable functions \alpha:[0,1]\to[0,1]. For each function \alpha, \mathcal{R}^{(\alpha)}, has the law of the range of a special subordinator. Constant functions correspond to stable su...

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Bibliographic Details
Published inAnnales de l'I.H.P. Probabilités et statistiques Vol. 51; no. 2; pp. 533 - 544
Main Author Marchal, P.
Format Journal Article
LanguageEnglish
Published Institut Henri Poincaré 01.05.2015
Subjects
60G51
Bernstein function
Regenerative set
Subordinator
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Summary:We construct, on a single probability space, a class of regenerative sets \mathcal{R}^{(\alpha)}, indexed by all measurable functions \alpha:[0,1]\to[0,1]. For each function \alpha, \mathcal{R}^{(\alpha)}, has the law of the range of a special subordinator. Constant functions correspond to stable subordinators. If \alpha\leq\beta, then \mathcal{R}^{(\alpha)}\subset\mathcal{R}^{(\beta)}. Other examples of special subordinators are given in the lattice case.
ISSN:0246-0203
DOI:10.1214/13-AIHP595