2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114115We estimate a median of $f(X_t)$ where $f$ is a Lipschitz function, $X$ is a Lévy process and $t$ an arbitrary time. This leads to concentration inequalities for $f(X_t)$. In turn, corresponding fluctuation estimates are obtained under assumptions typically satisfied if the process has a regular behavior in small time and a, possibly different, regular behavior in large time.Probability60E07, 60F10, 60G51,60G52text