Large deviations for clocks of self-similar processes

Nizar Demni (1) , Alain Rouault (2) , Marguerite Zani (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMV - Laboratoire de Mathématiques de Versailles
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a Lévy process drifting to ∞ and its inverse, the clock of the corresponding positive self-similar process. We describe here asymptotical properties of these clocks in large time, extending the results of [27].

Mots clés: self-similar processes; large deviations

Domaines: Probabilités [math.PR]

Nizar Demni, Alain Rouault, Marguerite Zani. Large deviations for clocks of self-similar processes. Catherine Donati-Martin; Antoine Lejay; Alain Rouault. In Memoriam Marc Yor : Séminaire de Probabilités XLVII, 2137, Springer, pp.443-466, 2015, Lecture Notes in Mathematics, 978-3-319-18584-2. ⟨10.1007/978-3-319-18585-9_19⟩. ⟨hal-01081795⟩