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Large deviations for dynamical Schrödinger problems
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DOI：10.1017/jpr.2025.10049.png)
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Abstract
En 中文
We establish large deviations for dynamical Schr & ouml;dinger problems driven by perturbed Brownian motions when the noise parameter tends to zero. Our results show that Schr & ouml;dinger bridges charge exponentially small masses outside the support of the limiting law that agrees with the optimal solution to the dynamical Monge-Kantorovich optimal transport problem. Our proofs build on mixture representations of Schr & ouml;dinger bridges and establishing exponential continuity of Brownian bridges with respect to the initial and terminal points.
Keywords:
Dynamical Schr & ouml
dinger problem
entropic optimal transport
large deviation
Schr & ouml
dinger bridge