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Median, Concentration and Fluctuation for Lévy Processes

C. Houdré·P. Marchal
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Abstract

We 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.

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C. Houdré, P. Marchal. 2006-07-03. Median, Concentration and Fluctuation for Lévy Processes. https://arxiv.org/abs/math/0607022

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