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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.


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