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Large Deviations for Clocks of Self-similar Processes

  • Nizar Demni
  • Alain Rouault
  • Marguerite Zani
Part of the Lecture Notes in Mathematics book series (LNM, volume 2137)

Abstract

The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a Lévy process drifting to \(\infty\) 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 Yor and Zani (Bernoulli 7, 351–362, 2001).

Notes

Acknowledgements

The authors want to thank Frédérique Petit for valuable conversations on the Cauchy clock.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut de Recherche Mathematiques de RennesRennesFrance
  2. 2.Université Versailles-Saint-Quentin, LMV UMR 8100, Bâtiment FermatVersailles-CedexFrance
  3. 3.Université d’OrléansUFR Sciences, Bâtiment de mathématiquesOrléans Cedex 2France

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