Malliavin calculus approach to long exit times from an unstable equilibrium

Yuri Bakhtin, Zsolt Pajor-Gyulai

Research output: Contribution to journalArticle

Abstract

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
Volume29
Issue number2
DOIs
StatePublished - Apr 1 2019

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Exit Time
Malliavin Calculus
Tail
Vector Field
Unstable
Exit
Malliavin calculus

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Malliavin calculus approach to long exit times from an unstable equilibrium. / Bakhtin, Yuri; Pajor-Gyulai, Zsolt.

In: Annals of Applied Probability, Vol. 29, No. 2, 01.04.2019, p. 827-850.

Research output: Contribution to journalArticle

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