Cram\'er's estimate for stable processes with power drift
Probability
2018-06-05 v1
Abstract
We investigate the upper tail probabilities of the all-time maximum of a stable L\'evy process with a power negative drift. The asymptotic behaviour is shown to be exponential in the spectrally negative case and polynomial otherwise, with explicit exponents and constants. Analogous results are obtained, at a less precise level, for the fractionally integrated stable L\'evy process. We also study the lower tail probabilities of the integrated stable L\'evy process in the presence of a power positive drift.
Cite
@article{arxiv.1806.00745,
title = {Cram\'er's estimate for stable processes with power drift},
author = {Christophe Profeta and Thomas Simon},
journal= {arXiv preprint arXiv:1806.00745},
year = {2018}
}