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