Malliavin calculus approach to long exit times from an unstable equilibrium

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. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.

Original languageEnglish (US)
Pages (from-to)827-850
Number of pages24
JournalAnnals of Applied Probability
Issue number2
StatePublished - Apr 2019


  • Exit problem
  • Malliavin calculus
  • Polynomial decay
  • Unstable equilibrium
  • Vanishing noise limit

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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