Median,concentration and fluctuations for Lévy processes |
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Authors: | Christian Houdré ,Philippe Marchal |
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Affiliation: | 1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;2. DMA, École Normale Supérieure, 75005 Paris, France |
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Abstract: | We estimate a median of f(Xt) where f is a Lipschitz function, X is a Lévy process and t is 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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Keywords: | 60E07 60F10 60G51 60G52 |
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