English

Median, Concentration and Fluctuation for L\'evy Processes

Probability 2007-05-23 v1

Abstract

We estimate a median of f(Xt)f(X_t) where ff is a Lipschitz function, XX is a L\'evy process and tt an arbitrary time. This leads to concentration inequalities for f(Xt)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.

Keywords

Cite

@article{arxiv.math/0607022,
  title  = {Median, Concentration and Fluctuation for L\'evy Processes},
  author = {C. Houdré and P. Marchal},
  journal= {arXiv preprint arXiv:math/0607022},
  year   = {2007}
}