NONEXPONENTIAL SANOV AND SCHILDER THEOREMS ON WIENER SPACE: BSDES, SCHRODINGER PROBLEMS AND CONTROL

• 成果类型: Article
• 署名作者: Backhoff-Veraguas, Julio; Lacker, Daniel; Tangpi, Ludovic
• 署名单位: University of Vienna; Columbia University; Princeton University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1531
• 发表日期: 2020
• 页码: 1321-1367
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; minimal supersolutions; VISCOSITY SOLUTIONS; large deviations; REPRESENTATION; limit

摘要

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.