Malliavin calculus approach to long exit times from an unstable equilibrium

Yuri Bakhtin; Zsolt Pajor-Gyulai

doi:10.1214/18-AAP1387

Malliavin calculus approach to long exit times from an unstable equilibrium

Yuri Bakhtin, Zsolt Pajor-Gyulai

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	827-850
Number of pages	24
Journal	Annals of Applied Probability
Volume	29
Issue number	2
DOIs	https://doi.org/10.1214/18-AAP1387
State	Published - Apr 2019

Keywords

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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10.1214/18-AAP1387

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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.",

keywords = "Exit problem, Malliavin calculus, Polynomial decay, Unstable equilibrium, Vanishing noise limit",

author = "Yuri Bakhtin and Zsolt Pajor-Gyulai",

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year = "2019",

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AU - Pajor-Gyulai, Zsolt

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N2 - 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.

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KW - Malliavin calculus

KW - Polynomial decay

KW - Unstable equilibrium

KW - Vanishing noise limit

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Malliavin calculus approach to long exit times from an unstable equilibrium

Abstract

Keywords

ASJC Scopus subject areas

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