Biomedical Imaging GroupSTI
English only   BIG > Publications > Lévy Processes

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

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.

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

© 2020 Springer. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Springer.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.