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Probability Theory and Related Fields

, Volume 135, Issue 2, pp 201–215 | Cite as

Inversion de l'espace et du temps des processus de Lévy stables

  • S. FouratiEmail author
Article

Abstract

We proove a new duality relation between stable Lévy processes with index Open image in new window and those with index Open image in new window . This duality appears to be the trajectorial version of the duality of Zolotarev which concerns one dimensional stable laws. We give an application of this result to the behaviour of the paths at small and large times of the process ``conditioned to stay positive''.

Mathematics Subject Classification

60G50 60G51 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Laboratoire de Probabilité et Modèles AléatoiresParis
  2. 2.CEDEX 05 et Laboratoire de Mathématique de L'INSAMont Saint AignanFrance

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