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

  • Julien Fageot
  • Michael Unser
  • John Paul WardEmail author
Article
  • 18 Downloads

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 \(n\)-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 

Mathematics Subject Classification (2010)

60G20 41A25 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Biomedical Imaging GroupÉcole polytechnique fédérale de Lausanne (EPFL)LausanneSwitzerland
  2. 2.Department of MathematicsNorth Carolina A&T State UniversityGreensboroUSA

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