Classical large deviation theorems on complete Riemannian manifolds

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Kraaij, Richard C.^1,2  Redig, Frank²  Versendaal, Rik² 

[1] Ruhr Univ Bochum, Fak Math, Postfach 102148, D-44721 Bochum, Germany

[2] Delft Univ Technol, Delft Inst Appl Math, POB 5031, NL-2600 GA Delft, Netherlands

关键词: Large deviations;    Cramer's theorem;    Geodesic random walks;    Riemannian Brownian motion;    Non-linear semigroup method;    Hamilton-Jacobi equation;   

DOI  :  10.1016/j.spa.2018.11.019

来源: Elsevier

【 摘 要 】

We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton-Jacobi equations. As a corollary, we also obtain the analogue of Cramer's theorem. The approach also provides a new proof of Schilder's theorem. Additionally, we provide a proof of Schilder's theorem by using an embedding into Euclidean space, together with Freidlin-Wentzell theory. (C) 2018 Published by Elsevier B.V.

【 授权许可】

Free