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.
@ARTICLE(http://bigwww.epfl.ch/publications/fageot2003.html, 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", number="1", pages="180--200", month="March", note="")