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arXiv · 2003.09281

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

Céline Duval·Ester Mariucci
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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.

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Céline Duval, Ester Mariucci. 2020-03-20. Non-asymptotic control of the cumulative distribution function of L\'evy processes. https://arxiv.org/abs/2003.09281

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