Persistence of integrated stable processes

2014/03/05 by Profeta, Christophe, Simon, Thomas · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1403.1064

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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