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

2025/06/21 by Mou, Chenchen, Qi, Weiwei, Shen, Zhongwei +1 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17546

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.

Citations

• On Limit Measures and Their Supports for Stochastic Ordinary Differential Equations
• Quasi-stationary distributions of multi-dimensional diffusion processes
• A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions
• More on the long time stability of Feynman-Kac semigroups
• General criteria for the study of quasi-stationarity
• Landscape and flux theory of non-equilibrium dynamical systems with application to biology
• Quasi-stationary distributions and diffusion models in population dynamics

Cited by

• DeepWKB: Learning WKB Expansions of Invariant Distributions for Stochastic Systems

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