Nonspectral modes and how to find them in the Ornstein-Uhlenbeck process with white μ-stable noise.

Thiel, F; Sokolov, I M; Postnikov, E B · Phys Rev E · 2016

basic_science · Level V

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Abstract

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.