Classical large deviation theorems on complete Riemannian manifolds
| Autor: | Frank Redig, Richard C. Kraaij, Rik Versendaal |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Statistics and Probability Pure mathematics Cramér's theorem Geodesic FOS: Physical sciences Cramer's theorem 01 natural sciences Hamilton–Jacobi equation 010104 statistics & probability Corollary Mathematics::Probability FOS: Mathematics Non-linear semigroup method 0101 mathematics Mathematical Physics Mathematics Euclidean space Applied Mathematics Probability (math.PR) 010102 general mathematics Mathematical Physics (math-ph) 60F10 58J65 60J99 Random walk Geodesic random walks Riemannian Brownian motion Large deviations Differential Geometry (math.DG) Modeling and Simulation Embedding Large deviations theory Mathematics - Probability |
| Zdroj: | Stochastic Processes and their Applications, 129(11) |
| ISSN: | 0304-4149 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect