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Quasi-potential of stationary and quasi-stationary densities: existence, regularity, and applications (2506.17546v1)
Published 21 Jun 2025 in math.DS
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.
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