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Compressibility of Symmetric-α-Stable Processes

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

Proceedings of the Eleventh International Workshop on Sampling Theory and Applications (SampTA'15), Washington DC, USA, May 25-29, 2015, pp. 236-240.

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. First, we characterize the Besov regularity of SαS processes. Then the n-term approximation rates follow. To capture the local smoothness behavior, we consider sparse processes defined on the circle that are solutions of stochastic differential equations.

AUTHOR="Ward, J.P. and Fageot, J. and Unser, M.",
TITLE="Compressibility of Symmetric-$\alpha$-Stable Processes",
BOOKTITLE="Proceedings of the Eleventh International Workshop on
        Sampling Theory and Applications ({SampTA'15})",
address="Washington DC, USA",
month="May 25-29,",

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