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تسجيل مستخدم جديدThe n-term Approximation of Periodic Generalized Levy Processes
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In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by $d$-dimensional periodic Levy white noises. Our results are based on the estimation of the Besov regularity of Levy white noises and generalized Levy processes. We show in particular that non-Gaussian generalized Levy processes are more compressible in a wavelet basis than the corresponding Gaussian processes, in the sense that their $n$-term approximation error decays faster. We quantify this compressibility in terms of the Blumenthal-Getoor index of the underlying Levy white noise.
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