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April 2019 Malliavin calculus approach to long exit times from an unstable equilibrium
Yuri Bakhtin, Zsolt Pajor-Gyulai
Ann. Appl. Probab. 29(2): 827-850 (April 2019). DOI: 10.1214/18-AAP1387

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.

Citation

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Yuri Bakhtin. Zsolt Pajor-Gyulai. "Malliavin calculus approach to long exit times from an unstable equilibrium." Ann. Appl. Probab. 29 (2) 827 - 850, April 2019. https://doi.org/10.1214/18-AAP1387

Information

Received: 1 October 2017; Revised: 1 February 2018; Published: April 2019
First available in Project Euclid: 24 January 2019

zbMATH: 07047439
MathSciNet: MR3910018
Digital Object Identifier: 10.1214/18-AAP1387

Subjects:
Primary: 60H07, 60H10, 60J60

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 2 • April 2019
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