Long exit times near a repelling equilibrium

Yuri Bakhtin; Hong Bin Chen

doi:10.1214/20-AAP1599

Long exit times near a repelling equilibrium

Yuri Bakhtin, Hong Bin Chen

Mathematics

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

Abstract

For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.

Original language	English (US)
Pages (from-to)	594-624
Number of pages	31
Journal	Annals of Applied Probability
Volume	31
Issue number	2
DOIs	https://doi.org/10.1214/20-AAP1599
State	Published - Apr 2021

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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10.1214/20-AAP1599

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title = "Long exit times near a repelling equilibrium",

abstract = "For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.",

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

author = "Yuri Bakhtin and Chen, {Hong Bin}",

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year = "2021",

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KW - Polynomial decay

KW - Unstable equilibrium

KW - Vanishing noise limit

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Long exit times near a repelling equilibrium

Abstract

Keywords

ASJC Scopus subject areas

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