Work

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

Year: 2024

Type: article

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 $\infty$ 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.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2024.104478

Authors: Yanyan Hu, Richard C. Kraaij, Fubao Xi

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,420

Funders: National Natural Science Foundation of China, China Scholarship Council

Award: 机制切换随机系统及其应用