Nonspectral modes and how to find them in the Ornstein-Uhlenbeck process with white μ-stable noise.
We consider the Ornstein-Uhlenbeck process with a broad initial probability distribution (Lévy distribution), which exhibits so-called nonspectral modes. The relaxation rate of such modes differs from those determined from the parameters of the corresponding Fokker-Plank equation. The first nonspectral mode is shown to govern the relaxation process and allows for estimation of the initial distribution's Lévy index. A method based on continuous wavelet transformation is proposed to extract both (spectral and nonspectral) relaxation rates from a stochastic data sample.
Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
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Thiel
Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
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Sokolov
Department of Theoretical Physics, Kursk State University, Radishcheva Street, 33, 305000 Kursk, Russia.
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Postnikov