## Abstract

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 language | English (US) |
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Pages (from-to) | 1321-1367 |

Number of pages | 47 |

Journal | Annals of Applied Probability |

Volume | 30 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2020 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Keywords

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