Abstract
We discuss the existence of stationary states for subharmonic potentials , c < 2, under the actionof symmetric α-stable noises. We show analytically that the necessary condition for the existence of the steady state isc > 2 − α. Consequently, forharmonic (c = 2) andsuperharmonic potentials (c > 2) driven by any α-stable noise, steady states always exist. Stationary states are characterized by probabilitydensity functions for having a lighter tail than the noise distribution for superharmonic potentials (c > 2) and a heavier tail than the noise distribution for subharmonic ones. Monte Carlosimulations confirm the existence of such stationary states and the form of the tails of thecorresponding probability densities.
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