Large deviations for slow-fast processes on connected complete Riemannian manifolds
arxiv(2024)
摘要
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 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.
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