The n-Term Approximation of Periodic Generalized Lévy Processes

J. Fageot, M. Unser, J.P. Ward

Journal of Theoretical Probability, vol. 33, no. 1, pp. 180-200, March 2020.

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.

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AUTHOR="Fageot, J. and Unser, M. and Ward, J.P.",
TITLE="The $n$-Term Approximation of Periodic Generalized {L}{\'{e}}vy
        Processes",
JOURNAL="Journal of Theoretical Probability",
YEAR="2020",
volume="33",
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pages="180--200",
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