Probability Theory and Related Fields

, Volume 110, Issue 1, pp 13–49 | Cite as

Points de croissance des processus de Lévy et théorie générale des processus

  • S. Fourati


We prove a conjecture of J. Bertoin: a Lévy process has increase times if and only if the integral \(\) is finite, where G and H are the distribution functions of the minimum and the maximum of the Lévy process killed at an independent exponential time. The “if” part of the statement had been obtained before by R. Doney. Our proof uses different techniques, from potential theory and the general theory of processes, and is self-contained. Our results also show that if P(X t <0)≤1/2 for all t small enough, then the process does not have increase times.

AMS Subject Classification (1991): Primary 60J30; Secondary 60G07 60J55 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • S. Fourati
    • 1
  1. 1.Analyse et Modèles Stochastiques, UPRES-A CNRS 6085, INSA de Rouen, F-76130 Mt. St. Aignan, FranceFR

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