Tails of exit times from unstable equilibria on the line

Yuri Bakhtin, Zsolt Pajor-Gyulai

Published 2018-10-12Version 1

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.