Median, concentration and fluctuations for Lévy processes

Christian Houdré and Philippe Marchal

Stochastic Processes and their Applications, 2008, vol. 118, issue 5, 852-863

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.

Keywords: Lévy; processes; Median; Fluctuations; Concentration (search for similar items in EconPapers)
Date: 2008
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