## The Annals of Applied Probability

### Malliavin calculus approach to long exit times from an unstable equilibrium

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 29, Number 2 (2019), 827-850.

Dates
Revised: February 2018
First available in Project Euclid: 24 January 2019

https://projecteuclid.org/euclid.aoap/1548298931

Digital Object Identifier
doi:10.1214/18-AAP1387

Mathematical Reviews number (MathSciNet)
MR3910018

Zentralblatt MATH identifier
07047439

#### Citation

Bakhtin, Yuri; Pajor-Gyulai, Zsolt. Malliavin calculus approach to long exit times from an unstable equilibrium. Ann. Appl. Probab. 29 (2019), no. 2, 827--850. doi:10.1214/18-AAP1387. https://projecteuclid.org/euclid.aoap/1548298931

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