Nonexponential sanov and schilder theorems on wiener space: Bsdes, schrödinger problems and 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 Schrödinger problem as an optimal transport cost, unifying the control-theoretic and probabilistic approaches initiated respectively by T. Mikami and C. Léonard. 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 Boué-Dupuis) for the Laplace transform of Wiener measure.

Original languageEnglish (US)
Pages (from-to)1321-1367
Number of pages47
JournalAnnals of Applied Probability
Issue number3
StatePublished - Jun 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • BSDE
  • Large deviations
  • Nonexponential
  • Sanov theorem
  • Schilder theorem
  • Schrödinger problem
  • Stochastic control
  • Wiener space


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