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Points de croissance des processus de Lévy et théorie générale des processus
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  • Published: January 1998

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

  • S. Fourati1 

Probability Theory and Related Fields volume 110, pages 13–49 (1998)Cite this article

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Summary.

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.

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Authors and Affiliations

  1. Analyse et Modèles Stochastiques, UPRES-A CNRS 6085, INSA de Rouen, F-76130 Mt. St. Aignan, France, , , , , , FR

    S. Fourati

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  1. S. Fourati
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Received: 4 May 1995/In revised form: 6 May 1997

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Fourati, S. Points de croissance des processus de Lévy et théorie générale des processus. Probab Theory Relat Fields 110, 13–49 (1998). https://doi.org/10.1007/s004400050143

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  • Issue Date: January 1998

  • DOI: https://doi.org/10.1007/s004400050143

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