Equilibrium of a confined, randomly-accelerated, inelastic particle: Is   there inelastic collapse?
  We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0<x<1. The reflections of the particle from the boundaries at x=0 and 1 are inelastic, with coefficient of restitution r. We have solved the Fokker-Planck equation satisfied by the equilibrium distribution function P(x,v) with a combination of exact analytical and numerical methods. Throughout the interval 0<r<1, P(x,v) remains extended, as opposed to collapsed. The particle is not localized at the boundary. However, for r<0.163 the equilibrium boundary collision rate is infinite, as predicted by Cornell et al., and all moments of the velocity just after reflection from the boundary vanish. 
Theodore W. Burkhardt and Stanislav N. Kotsev