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Article Dans Une Revue Probability Theory and Related Fields Année : 2015

Persistence of integrated stable processes

Résumé

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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hal-00955712 , version 1 (05-03-2014)

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Christophe Profeta, Thomas Simon. Persistence of integrated stable processes. Probability Theory and Related Fields, 2015, 162 (3), pp.463-485. ⟨hal-00955712⟩
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