Persistence of integrated stable processes

Christophe Profeta; Thomas Simon

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arXiv · 1403.1064

Persistence of integrated stable processes

Christophe Profeta·Thomas Simon

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Abstract

We compute the persistence exponent of the integral of a stable L\'evy 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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Christophe Profeta, Thomas Simon. 2014-03-05. Persistence of integrated stable processes. https://arxiv.org/abs/1403.1064

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