Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges - Archive ouverte HAL
Article Dans Une Revue Probability Theory and Related Fields Année : 2017

Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges

Résumé

In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the invariant measure are proven. All results are based on a seemingly new expression of the drift of a bridge in terms of the reciprocal characteristic, which, roughly speaking, quantifies the “mean acceleration” of a bridge.
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Dates et versions

hal-01650189 , version 1 (28-11-2017)

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Giovanni Conforti, Max-K. von Renesse. Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges. Probability Theory and Related Fields, In press, ⟨10.1007/s00440-017-0814-9⟩. ⟨hal-01650189⟩
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