  We estimate a median of $f(X_t)$ where $f$ is a Lipschitz function, $X$ is a
L\'evy 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.
