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arXiv · 1806.00745

Cram\'er's estimate for stable processes with power drift

Christophe Profeta·Thomas Simon
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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.

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Christophe Profeta, Thomas Simon. 2018-06-03. Cram\'er's estimate for stable processes with power drift. https://arxiv.org/abs/1806.00745

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