Quasi-potential of stationary and quasi-stationary densities: existence, regularity, and applications

TL;DR

This paper investigates the regularity and existence of the quasi-potential for stationary and quasi-stationary densities in perturbed dynamical systems, providing a theoretical foundation for large deviation principles in complex attractor settings.

Contribution

It establishes the existence and regularity of the quasi-potential within a broad class of dynamical systems with general maximal attractors.

Findings

Proves the existence of the quasi-potential under broad conditions

Analyzes the regularity properties of the quasi-potential

Provides applications to large deviation principles in dynamical systems

Abstract

The present paper is devoted to the large deviation principle (LDP), with particular emphasis on the regularity of the quasi-potential for densities of stationary and quasi-stationary distributions of randomly perturbed dynamical systems. Our framework is set up within a positively invariant set contained in the basin of attraction of a maximal attractor of the unperturbed system. Such a setting with a general maximal attractor is anticipated in many applications.