Phase space analysis of the harmonic oscillatorwith Lévy noise: Spectral measure and deviation from ellipticity

摘要

We show that the location and velocity of the harmonic oscillator with Lévy-stable noise are mutually Lévy-stable distributed. We give explicitly the associated spectral measure, exhibiting both the non independence and the non ellipticity of the location-velocity couple. We then propose measures of deviation from ellipticity.