Scaling Limit for the Diffusion Exit Problem in the Levinson Case

Details Scaling Limit for the Diffusion Exit Problem in the Levinson Case Scaling Limit for the Diffusion Exit Problem in the Levinson Case

2010-06-14

arxiv.org/abs/1006.2766v1

Mathematics

Probability

13 pages

Scientific paper

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 1-d diffusions conditioned on rare events.

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