Phase Space Analysis of the Harmonic Oscillator with Lévy Noise: Spectral Measure and Deviation from Ellipticity

Steeve Zozor (1) , Christophe Vignat (2, 3)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 LTHI - Information Theory Laboratory (LTHI)
3 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Steeve Zozor, Christophe Vignat. Phase Space Analysis of the Harmonic Oscillator with Lévy Noise: Spectral Measure and Deviation from Ellipticity. EUSIPCO 2011 - 19th European Signal Processing Conference, Aug 2011, Barcelone, Spain. pp.2239-2243. ⟨hal-00623694⟩