A second order SDE for the Langevin process reflected at a completely   inelastic boundary
  It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog. 
Jean Bertoin (PMA, DMA)