Scaling limits for the exit problem for conditioned diffusions via Hamilton-Jacobi equations

Series: 
Stochastics Seminar
Thursday, September 12, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
GaTech
Organizer: 
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.