Spectral measure of the harmonic oscillator with α-stable noise

Abstract : We study the coordinate-velocity couple of the harmonic oscillator with α-stable noise. As previously shown by Sokolov et al., the distribution of this couple is bivariate α-stable. In this work, we determine explicitly its associated spectral measure, exhibiting directly both the non-independence and non-ellipticity of the coordinate- velocity couple. Knowledge of the spectral measure allows to analyze and quantify the deviation from ellipticity.
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https://hal.archives-ouvertes.fr/hal-00623692
Contributor : Steeve Zozor <>
Submitted on : Wednesday, September 14, 2011 - 9:38:43 PM
Last modification on : Monday, April 9, 2018 - 12:22:45 PM

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Steeve Zozor, Christophe Vignat. Spectral measure of the harmonic oscillator with α-stable noise. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2011, 84 (3), pp.031115. ⟨10.1103/PhysRevE.84.031115⟩. ⟨hal-00623692⟩

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