Spectral measure of the harmonic oscillator with α-stable noise
Résumé
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.