Translator Disclaimer
2019 Cramér’s estimate for stable processes with power drift
Christophe Profeta, Thomas Simon
Electron. J. Probab. 24: 1-21 (2019). DOI: 10.1214/19-EJP275

Abstract

We investigate the upper tail probabilities of the all-time maximum of a stable Lévy 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 Lévy process. We also study the lower tail probabilities of the integrated stable Lévy process in the presence of a power positive drift.

Citation

Download Citation

Christophe Profeta. Thomas Simon. "Cramér’s estimate for stable processes with power drift." Electron. J. Probab. 24 1 - 21, 2019. https://doi.org/10.1214/19-EJP275

Information

Received: 26 June 2018; Accepted: 4 February 2019; Published: 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07055655
MathSciNet: MR3925457
Digital Object Identifier: 10.1214/19-EJP275

Subjects:
Primary: 60G18, 60G22, 60G51, 60G52, 60G70

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.24 • 2019
Back to Top