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June 2020 Nonexponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger problems and control
Julio Backhoff-Veraguas, Daniel Lacker, Ludovic Tangpi
Ann. Appl. Probab. 30(3): 1321-1367 (June 2020). DOI: 10.1214/19-AAP1531

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.

Citation

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Julio Backhoff-Veraguas. Daniel Lacker. Ludovic Tangpi. "Nonexponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger problems and control." Ann. Appl. Probab. 30 (3) 1321 - 1367, June 2020. https://doi.org/10.1214/19-AAP1531

Information

Received: 1 October 2018; Revised: 1 June 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

MathSciNet: MR4133375
Digital Object Identifier: 10.1214/19-AAP1531

Subjects:
Primary: 60F10, 60H30, 93E03

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 3 • June 2020
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