Non-asymptotic control of the cumulative distribution function of Lévy processes
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.
READ FULL TEXT