Large deviation estimates for reflected stochastic processes: a PDE approach

Abstract: We prove Freidlin-Wentzell type estimates for random perturbations of nonstationnary dynamical systems with Lipschitz continuous oblique reflections on smooth boundaries. Our proof is based on a Partial Differential Equations approach : the small perturbation which we want to estimate is the viscosity solution of an Hamilton-Jacobi-Bellman equation. When passing to the limit as the random perturbation goes to zero, we obtain, by using the uniqueness of the solution of the limiting equation, a representation formula for the limiting solution in terms of the action functional.
Helge Holden <holden@math.ntnu.no>
2001-12-03 09:11