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

Jean Bertoin (2008)

Journal of the European Mathematical Society

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.

Additive functionals of Markov processes and stochastic systems

Evgeny B. Dynkin (1975)

Annales de l'institut Fourier

Intuitively, an additive functional of a stochastic process ( x t , P ) gives a method to measure time taking into account the development of the process. We associate with any set of states C the mathematical expectation of time x t belongs to C . In this way, we establish to one-to-one correspondence between all the normal additive functionals of a Markov process and all the δ -finite measures on the state space which charge no inaccessible set. This is proved under the condition that transition probabilities...

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