Scaling limit for the diffusion exit problem in the Levinson case

Sergio Angel Almada Monter and Yuri Bakhtin

Stochastic Processes and their Applications, 2011, vol. 121, issue 1, 24-37

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.

Keywords: Small; noise; Exit; problem; Levinson; case; Rare; event (search for similar items in EconPapers)
Date: 2011
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