Classical large deviation theorems on complete Riemannian manifolds

Richard C. Kraaij, Frank Redig and Rik Versendaal

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4294-4334

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.

Keywords: Large deviations; Cramér’s theorem; Geodesic random walks; Riemannian Brownian motion; Non-linear semigroup method; Hamilton–Jacobi equation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2018.11.019

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