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.
Original language | English |
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Pages (from-to) | 4294-4334 |
Number of pages | 41 |
Journal | Stochastic Processes and their Applications |
Volume | 129 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2019 |
Bibliographical note
Accepted author manuscriptKeywords
- Cramér's theorem
- Geodesic random walks
- Hamilton–Jacobi equation
- Large deviations
- Non-linear semigroup method
- Riemannian Brownian motion