In this paper, we establish a moderate deviation principle for the Langevin dynamics with strong damping. The weak convergence approach plays an important role in the proof.
Keyword: Stochastic Langevin equation Large deviations Moderate deviations.MSC: 60H10 60F10.
In this paper, we find some general and efficient sufficient conditions for the exponential convergence W 1,d (P t (x, •), P t (y, •)) ≤ Ke −δt d(x, y) for the semigroup (P t ) of one-dimensional diffusion. Moreover some sharp estimates of the involved constants K ≥ 1, δ > 0 are provided. Those general results are illustrated by a series of examples.
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