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A second order SDE for the Langevin process reflected at a completely inelastic boundary. (English) Zbl 1169.60009

Author’s abstract: It was shown in [J. Bertoin, Ann. Probab. 35, No. 6, 2021–2037 (2007; Zbl 1132.60057)] 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G44 Martingales with continuous parameter
60G40 Stopping times; optimal stopping problems; gambling theory

Citations:

Zbl 1132.60057
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References:

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