Persistence of integrated stable processes
Probability
2014-03-06 v1
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.
Keywords
Cite
@article{arxiv.1403.1064,
title = {Persistence of integrated stable processes},
author = {Christophe Profeta and Thomas Simon},
journal= {arXiv preprint arXiv:1403.1064},
year = {2014}
}