Persistence of integrated stable processes

Abstract : We compute the persistence exponent of the integral of a stable Lévy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Z. Shi (2003). Along the way, we investigate the law of the stable process L evaluated at the first time its integral X hits zero, when the bivariate process (X,L) starts from a coordinate axis. This extends classical formulae by McKean (1963) and Gor'kov (1975) for integrated Brownian motion.
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https://hal.archives-ouvertes.fr/hal-00955712
Contributor : Christophe Profeta <>
Submitted on : Wednesday, March 5, 2014 - 9:56:53 AM
Last modification on : Tuesday, July 3, 2018 - 11:23:07 AM
Long-term archiving on : Thursday, June 5, 2014 - 11:00:41 AM

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  • HAL Id : hal-00955712, version 1
  • ARXIV : 1403.1064

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Christophe Profeta, Thomas Simon. Persistence of integrated stable processes. 2014. ⟨hal-00955712⟩

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