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Non-asymptotic control of the cumulative distribution function of Lévy processes
Published online by Cambridge University Press: 15 June 2022
Abstract
We propose non-asymptotic controls of the cumulative distribution function
$\mathbb{P}(|X_{t}|\ge \varepsilon)$
, for any
$t>0$
,
$\varepsilon>0$
and any Lévy process X such that its Lévy density is bounded from above by the density of an
$\alpha$
-stable-type Lévy process in a neighborhood of the origin.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust