Large Deviations Principle by viscosity solutions: The case of diffusions with oblique Lipschitz reflections

Magdalena Kobylanski (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular do- mains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.

Mots clés: Large Deviations Principle; Diffusions with oblique reflections; Viscosity solutions; Optimal control; Optimal stopping

Domaines: Probabilités [math.PR]

Magdalena Kobylanski. Large Deviations Principle by viscosity solutions: The case of diffusions with oblique Lipschitz reflections. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (1), pp.160-181. ⟨hal-00795367⟩