PHASE SPACE ANALYSIS OF THE HARMONIC OSCILLATOR WITH LéVY NOISE: SPECTRAL MEASURE AND DEVIATION FROM ELLIPTICITY

摘要

We show that the location and velocity of the harmonic oscillatorwith L′evy-stable noise are mutually L′evy-stable distributed.We give explicitly the associated spectral measure,exhibiting both the non independence and the non ellipticityof the location-velocity couple. We then propose measuresof deviation from ellipticity.