Scaling limit for the diffusion exit problem in the Levinson case

Sergio Angel Almada Monter, Yuri Bakhtin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)24-37
Number of pages14
JournalStochastic Processes and their Applications
Issue number1
StatePublished - Jan 2011


  • Exit problem
  • Levinson case
  • Rare event
  • Small noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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