Reflecting a Langevin process at an absorbing boundary

We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the particle can be in-stantaneously reflected, and study some properties of this reflecting solution. 1. Introduction. Langevin [9] introduced a probabilistic model to describe the evolution of a particle under random external forcing. Langevin’s motion has smooth trajectories, in the sense that if Yt stands for the position of the particle at time t, then the velocity Ẏt: = dYt/dt is well defined and finite everywhere. We assume that the external force (i.e., the derivative of the velocity) is a white noise