Scaling Limit for the Diffusion Exit Problem in the Levinson Case
Abstract
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the driving vector field and the initial condition, and each of the components of the perturbation follows a scaling limit. We derive the joint scaling limit for the random exit time and exit point. We use this result to study the asymptotics of the exit time for 1d diffusions conditioned on rare events.
 Publication:

arXiv eprints
 Pub Date:
 June 2010
 arXiv:
 arXiv:1006.2766
 Bibcode:
 2010arXiv1006.2766A
 Keywords:

 Mathematics  Probability;
 Mathematics  Dynamical Systems;
 60H10;
 60J60
 EPrint:
 13 pages