JournalsjemsVol. 10 , No. 3DOI 10.4171/jems/125

A second order SDE for the Langevin process reflected at a completely inelastic boundary

  • Jean Bertoin

    Universität Zürich, Switzerland
A second order SDE for the Langevin process reflected at a completely inelastic boundary cover

Abstract

It was shown in \cite{Be} 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.