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

F. Thiel, I. M. Sokolov, E. B. Postnikov

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5 Scopus citations

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.

Original languageEnglish
Article number052104
JournalPhysical Review E
Volume93
Issue number5
DOIs
StatePublished - 2 May 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 American Physical Society.

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