Classical large deviation theorems on complete Riemannian manifolds
Richard C. Kraaij (Ruhr-Universität Bochum)
Frank Redig (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Rik Versendaal (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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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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