Non-asymptotic control of the cumulative distribution function of Lévy processes

03/20/2020

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by   Céline Duval, et al.

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We propose non-asymptotic controls of the cumulative distribution function P(|X_t|>ε), for any t>0, ε>0 and any Lévy process X such that its Lévy density is bounded from above by the density of an α-stable type Lévy process in a neighborhood of the origin. The results presented are non-asymptotic and optimal, they apply to a large class of Lévy processes.