 Large deviations for slow–fast processes on connected complete Riemannian manifoldsYanyan Hu, Richard C. Kraaij and Fubao Xi Stochastic Processes and their Applications, 2024, vol. 178, issue C Abstract: We consider a class of slow–fast processes on a connected complete Riemannian manifold M. The limiting dynamics as the scale separation goes to ∞ 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 Hamilton–Jacobi–Bellman (HJB) equation techniques. Our main innovation is solving the comparison principle for viscosity solutions for the HJB equation on M and the construction of a variational viscosity solution for the non-smooth Hamiltonian, which lies at the heart of deriving the action integral representation for the rate function. Keywords: Riemannian manifold; Large deviation principle; Hamilton–Jacobi–Bellman equations; Comparison principle; Action-integral representation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001844 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104478 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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