Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections (Q1943324)

A reflected diffusion in a bounded domain perturbed by small noise is considered. A Freidlin-Wentzell type large deviations principle is proved in the small noise limit, identifying a good rate function as the value function of an associated deterministic control problem. The method uses log-transformation to convert the partial differential equations satisfied by the relevant probabilities into Hamilton-Jacobi-Bellman equations and then passing to the small noise limit in the latter to find a viscosity solution of the limiting Hamilton-Jacobi equation.