Fageot, JulienUnser, MichaelWard, John Paul2020-05-202020-05-202020-05-202020-03-0110.1007/s10959-018-00877-7https://infoscience.epfl.ch/handle/20.500.14299/168820WOS:000530548400008In 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 errors decay faster. We quantify this compressibility in terms of the Blumenthal-Getoor indices of the underlying Levy white noise.Statistics & ProbabilityMathematicsgeneralized levy processeslevy white noisesbesov regularityn-term approximationcompressibilitysample pathsspacestext::journal::journal article::research article