Abstract
We consider regularity properties of the quasipotential function V defined by A. D. Ventcel and M. I. Freidlin in their work on asymptotically small random perturbations of stable dynamical systems. The regularity properties of V are important for the success of various asymptotic calculations carried out in the literature. Employing classical techniques from the calculus of variations and differential equations, we prove various results about the smoothness of V and its level sets. Among other things, there exists a dense connected open set, containing the stable point for the underlying dynamical system, in which V is continuously differentiable to the same degree as the Lagrangian involved in the defining variational problem.
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Communicated by W. Fleming
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Day, M.V., Darden, T.A. Some regularity results on the Ventcel-Freidlin quasi-potential function. Appl Math Optim 13, 259–282 (1985). https://doi.org/10.1007/BF01442211
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DOI: https://doi.org/10.1007/BF01442211