Tails of exit times from unstable equilibria on the line

Yuri Bakhtin, Zsolt Pajor-Gyulai

Research output: Contribution to journalArticlepeer-review


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. We also discuss our program on rare transitions in noisy heteroclinic networks.

Original languageEnglish (US)
Pages (from-to)477-496
Number of pages20
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 1 2020


  • Keywords: vanishing noise limit
  • exit problem
  • polynomial decay
  • unstable equilibrium

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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