Median, Concentration and Fluctuation for L\'evy Processes
Abstract
We estimate a median of f(Xt) where f is a Lipschitz function, X is a L\'evy process and t an arbitrary time. This leads to concentration inequalities for f(Xt). 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.
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