Reflecting a Langevin process at an absorbing boundary
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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 instantaneously reflected, and study some properties of this reflecting solution. DOI: https://doi.org/10.1214/009117906000001213 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-78182 Published Version Originally published at: Bertoin, Jean (2007). Reflecting a Langevin process at an absorbing boundary. The Annals of Probability, 35(6):2021-2037. DOI: https://doi.org/10.1214/009117906000001213 The Annals of Probability 2007, Vol. 35, No. 6, 2021–2037 DOI: 10.1214/009117906000001213 © Institute of Mathematical Statistics, 2007 REFLECTING A LANGEVIN PROCESS AT AN ABSORBING BOUNDARY
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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...
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تاریخ انتشار 2017