The $$n$$n-term Approximation of Periodic Generalized Lévy Processes

Julien Fageot, Michael Unser and John Paul Ward ()
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Julien Fageot: École polytechnique fédérale de Lausanne (EPFL)
Michael Unser: École polytechnique fédérale de Lausanne (EPFL)
John Paul Ward: North Carolina A&T State University

Journal of Theoretical Probability, 2020, vol. 33, issue 1, 180-200

Abstract: 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 $$n$$n-term approximation errors decay faster. We quantify this compressibility in terms of the Blumenthal–Getoor indices of the underlying Lévy white noise.

Keywords: Generalized Lévy processes; Lévy white noises; Besov regularity; n-term approximation; Compressibility; 60G20; 41A25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-018-00877-7

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