Tails of exit times from unstable equilibria on the line

Abstract

For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.

20 pages; the main difference with the previous version is a new section on noisy heteroclinic networks which are the main motivation for the present study

Cited by in corpus (2)

• Long exit times near a repelling equilibrium
• Atypical exit events near a repelling equilibrium