The n-term Approximation of Periodic Generalized Lévy Processes
J. Fageot, M. Unser, J.P. Ward
Journal of Theoretical Probability, in press.
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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 errors decay faster. We quantify this compressibility in terms of the Blumenthal-Getoor indices of the underlying Lévy white noise.