Journal
ANNALS OF APPLIED PROBABILITY
Volume 30, Issue 3, Pages 1321-1367Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/19-AAP1531
Keywords
Large deviations; Wiener space; Sanov theorem; Schilder theorem; nonexponential; BSDE; Schrodinger problem; stochastic control
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We derive new limit theorems for Brownian motion, which can be seen as nonexponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits of backward stochastic differential equations and their related partial differential equations. As a second application, we extend prior results on the small-noise limit of the Schrodinger problem as an optimal transport cost, unifying the control-theoretic and probabilistic approaches initiated respectively by T. Mikami and C. Leonard. Lastly, our results suggest a new scheme for the computation of mean field optimal control problems, distinct from the conventional particle approximation. A key ingredient in our analysis is an extension of the classical variational formula (often attributed to Borell or Boue-Dupuis) for the Laplace transform of Wiener measure.
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