## Non-asymptotic control of the cumulative distribution function of L\'evy processes

### Abstract

We propose non-asymptotic controls of the cumulative distribution function $P(|X_{t}|\ge \varepsilon)$, for any $t>0$, $\varepsilon>0$ and any L\'evy process $X$ such that its L\'evy density is bounded from above by the density of an $\alpha$-stable type L\'evy process in a neighborhood of the origin. The results presented are non-asymptotic and optimal, they apply to a large class of L\'evy processes

Topics: Mathematics - Probability, Mathematics - Statistics Theory
Year: 2020
OAI identifier: oai:arXiv.org:2003.09281

### Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.