We give a new PDE proof of a Freidlin-Wentzell theorem about the exit points from a domain of a random process, obtained by perturbing a dynamical system through the addition of a small noise. The relevant part of the analysis concerns an Hamilton-Jacobi equation, coupled with a Neumann boundary condition, which does not possess any strict subsolution. A metric method based on the introduction of an intrinsic length is adopted, and a notion of Aubry set, adjusted to the setting, is given.
Randomly perturbed dynamical systems and Aubry-Mather theory / Camilli, Fabio; A., Cesaroni; Siconolfi, Antonio. - In: INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS. - ISSN 1752-3583. - 2:(2009), pp. 139-168. [10.1504/IJDSDE.2009.031100]
Randomly perturbed dynamical systems and Aubry-Mather theory
CAMILLI, FABIO;SICONOLFI, Antonio
2009
Abstract
We give a new PDE proof of a Freidlin-Wentzell theorem about the exit points from a domain of a random process, obtained by perturbing a dynamical system through the addition of a small noise. The relevant part of the analysis concerns an Hamilton-Jacobi equation, coupled with a Neumann boundary condition, which does not possess any strict subsolution. A metric method based on the introduction of an intrinsic length is adopted, and a notion of Aubry set, adjusted to the setting, is given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
