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Large deviations for dynamical Schr\"{o}dinger problems
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We establish large deviations for dynamical Schr\"{o}dinger problems driven by perturbed Brownian motions when the noise parameter tends to zero. Our results show that Schr\"{o}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\"{o}dinger bridges and establishing exponential continuity of Brownian bridges with respect to the initial and terminal points.
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Large deviations for scaled families of Schr\"odinger bridges with reflection
Large deviation principles for entropic optimal transport are generalized to Schrödinger bridges with uniformly convergent cost functions, covering reflected Brownian reference processes on bounded convex domains.
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