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Persistence of integrated stable processes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 30 Jul 2014Embargo end date: 01 Jan 2014 France Publisher:Springer Science and Business Media LLCJournal:Probability Theory and Related Fields, volume 162, pages 463-485 (issn: 0178-8051, eissn: 1432-2064,

Authors: Thomas Simon; Thomas Simon; Christophe Profeta;

doi: 10.1007/s00440-014-0577-5 , 10.48550/arxiv.1403.1064

arXiv: http://arxiv.org/abs/1403.1064

Persistence of integrated stable processes

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Abstract

We compute the persistence exponent of the integral of a stable L��vy 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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France

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Keywords

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Integrated process, Probability (math.PR), Stable Lévy process, Half-Cauchy distribution, Lower tail probability, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Persistence, Hitting place, FOS: Mathematics, 60J50, 60F99, Mellin transform, Mathematics - Probability, 60G52

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