Scaling Limit for the Diffusion Exit Problem in the Levinson Case

2010/06/14 by Monter, Sergio Angel Almada, Bakhtin, Yuri
#60H10 #60J60 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1006.2766

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 1-d diffusions conditioned on rare events.

Related

• Scaling Limit for the Diffusion Exit Problem
• Scaling Limit for the Diffusion Exit Problem, a Survey
• Scaling limit for escapes from unstable equilibria in the vanishing noise limit: nontrivial Jordan block case
• Persistence of Small Noise and Random initial conditions
• Exit Laws of Isotropic Diffusions in Random Environment from Large Domains