Article ID Journal Published Year Pages File Type
1156836 Stochastic Processes and their Applications 2011 14 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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