Classical large deviation theorems on complete Riemannian manifolds

Kraaij, R.C.; Redig, F.H.J.; Versendaal, R.

doi:10.1016/j.spa.2018.11.019

Classical large deviation theorems on complete Riemannian manifolds

Journal article (2019)

Authors

R.C. Kraaij Ruhr-Universität Bochum

F.H.J. Redig Applied Probability -

R. Versendaal Applied Probability -

Research Group

Applied Probability () (TU Delft)

DOI: https://doi.org/10.1016/j.spa.2018.11.019

Large deviations Hamilton–Jacobi equation Geodesic random walks Cramér's theorem Non-linear semigroup method Riemannian Brownian motion

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Published Date

2019

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

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 Cramér'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.

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