The Annals of Applied Probability

Malliavin calculus approach to long exit times from an unstable equilibrium

Yuri Bakhtin and Zsolt Pajor-Gyulai

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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
Received: October 2017
Revised: February 2018
First available in Project Euclid: 24 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1548298931

Digital Object Identifier
doi:10.1214/18-AAP1387

Mathematical Reviews number (MathSciNet)
MR3910018

Zentralblatt MATH identifier
07047439

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

Keywords
Vanishing noise limit unstable equilibrium exit problem polynomial decay Malliavin calculus

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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