The \(n\)-term Approximation of Periodic Generalized Lévy Processes


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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Funding was provided by the European Research Council (Grant No. 692726 - GlobalBioIm).

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Correspondence to John Paul Ward.

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Fageot, J., Unser, M. & Ward, J.P. The \(n\)-term Approximation of Periodic Generalized Lévy Processes. J Theor Probab 33, 180–200 (2020).

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  • Generalized Lévy processes
  • Lévy white noises
  • Besov regularity
  • n-term approximation
  • Compressibility

Mathematics Subject Classification (2010)

  • 60G20
  • 41A25