GENERALIZED LANGEVIN-EQUATIONS - ANOMALOUS DIFFUSION AND PROBABILITY-DISTRIBUTIONS

We study the motion of a particle governed by a generalized Langevin e quation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to supe rdiffusive, along with subdiffusive and diffusive. When the random for ce is Gaussian, we derive the exact equations for the joint and margin al probability density functions for the position and velocity of the particle and find their solutions.