The n-term Approximation of Periodic Generalized Lévy Processes
  In this paper, we study the compressibility of random processes and fields,
called generalized Lévy processes, that are solutions of stochastic
differential equations driven by $d$-dimensional periodic Lévy white noises.
Our results are based on the estimation of the Besov regularity of Lévy white
noises and generalized Lévy processes. We show in particular that
non-Gaussian generalized Lévy processes are more compressible in a wavelet
basis than the corresponding Gaussian processes, in the sense that their
$n$-term approximation error decays faster. We quantify this compressibility in
terms of the Blumenthal-Getoor index of the underlying Lévy white noise.
