The n-term Approximation of Periodic Generalized Levy Processes

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by $d$-dimensional periodic Levy white noises. Our results are based on the estimation of the Besov regularity of Levy white noises and generalized Levy processes. We show in particular that non-Gaussian generalized Levy 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 Levy white noise.