Article Dans Une Revue Electronic Journal of Probability Année : 2019

Cramér’s estimate for stable processes with power drift

Résumé

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.

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Dates et versions

hal-04346477 , version 1 (19-12-2023)

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Christophe Profeta, Thomas Simon. Cramér’s estimate for stable processes with power drift. Electronic Journal of Probability, 2019, 24, pp.275. ⟨10.1214/19-EJP275⟩. ⟨hal-04346477⟩
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