Georgia Institute of Technology College of Sciences

The classical Freidlin--Wentzell theory on small random perturbations of dynamical systems operates mainly at the level of large deviation estimates. In many cases it would be interesting and useful to supplement those with central limit theorem type results. We are able to describe a class of situations where a Gaussian scaling limit for the exit point of conditioned diffusions holds. Our main tools are Doob's h-transform and new gradient estimates for Hamilton--Jacobi equations. Joint work with Andrzej Swiech.