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Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges
Ist Teil von
Probability theory and related fields, 2018-10, Vol.172 (1-2), p.493-524
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2018
Link zum Volltext
Quelle
EBSCOhost Business Source Ultimate
Beschreibungen/Notizen
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.