Tails of exit times from unstable equilibria on the line
Probability
2020-07-22 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1810.05341,
title = {Tails of exit times from unstable equilibria on the line},
author = {Yuri Bakhtin and Zsolt Pajor-Gyulai},
journal= {arXiv preprint arXiv:1810.05341},
year = {2020}
}
Comments
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