Long exit times near a repelling equilibrium

Yuri Bakhtin, Hong Bin Chen

Research output: Contribution to journalArticlepeer-review


For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.

Original languageEnglish (US)
Pages (from-to)594-624
Number of pages31
JournalAnnals of Applied Probability
Issue number2
StatePublished - Apr 2021


  • 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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