Title: The n-term Approximation of Periodic Generalized Lévy Processes,
Abstract: 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.