Couplings, Gradient Estimates and Logarithmic Sobolev Inequality for Langevin Bridges

with Giovanni Conforti

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.