Large deviations for slow–fast processes on connected complete Riemannian manifolds

Yanyan Hu*, Richard C. Kraaij, Fubao Xi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article number104478
Number of pages24
JournalStochastic Processes and their Applications
Volume178
DOIs
Publication statusPublished - 2024

Keywords

  • Action-integral representation
  • Comparison principle
  • Hamilton–Jacobi–Bellman equations
  • Large deviation principle
  • Riemannian manifold

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