Classical large deviations theorems on complete Riemannian manifolds

Abstract

We generalize classical large deviations theorems to the setting of complete Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using visocity 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.

References in corpus (2)

• Large deviations for Markov jump processes with mean-field interaction via the comparison principle for an associated Hamilton-Jacobi equation
• Dynamical moderate deviations for the Curie-Weiss model

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• Large deviations for random walks on Lie groups