Large deviations for slow-fast processes on connected complete Riemannian manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914708211105792 |
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| author | Hu, Yanyan Kraaij, Richard C. Xi, Fubao |
| author_facet | Hu, Yanyan Kraaij, Richard C. Xi, Fubao |
| contents | We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation principles with an action-integral rate function for the slow process by nonlinear semigroup methods together with the Hamilton-Jacobi-Bellman equation techniques. The innovation is solving a comparison principle for viscosity solutions on $M$ and the existence of a viscosity solution via a control problem for a non-smooth Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations for slow-fast processes on connected complete Riemannian manifolds Hu, Yanyan Kraaij, Richard C. Xi, Fubao Probability 60F10, 60J25 (Primary) 60J35, 49L25 (Secondary) We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation principles with an action-integral rate function for the slow process by nonlinear semigroup methods together with the Hamilton-Jacobi-Bellman equation techniques. The innovation is solving a comparison principle for viscosity solutions on $M$ and the existence of a viscosity solution via a control problem for a non-smooth Hamiltonian. |
| title | Large deviations for slow-fast processes on connected complete Riemannian manifolds |
| topic | Probability 60F10, 60J25 (Primary) 60J35, 49L25 (Secondary) |
| url | https://arxiv.org/abs/2403.05505 |