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

It was shown in [J. Bertoin, Ann. Probab. 35, No. 6, 2021 132037] 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. DOI: https://doi.org/10.4171/JEMS/125 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-78172 Originally published at: Bertoin, J (2008). A second order SDE for the Langevin process reflected at a completely inelastic boundary. Journal of the European Mathematical Society, 10(3):625-639. DOI: https://doi.org/10.4171/JEMS/125 J. Eur. Math. Soc. 10, 625–639 c © European Mathematical Society 2008 Jean Bertoin A second order SDE for the Langevin process reflected at a completely inelastic boundary Received October 14, 2006 and in revised form December 22, 2006 Abstract. It was shown in [2] 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.