Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

Yuri Bakhtin; Alexisz Gaál

doi:10.1142/S0219493720500264

Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

Yuri Bakhtin, Alexisz Gaál

Mathematics

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

Abstract

We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus, this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.

Original language	English (US)
Article number	2050026
Journal	Stochastics and Dynamics
Volume	20
Issue number	4
DOIs	https://doi.org/10.1142/S0219493720500264
State	Published - Aug 1 2020

Keywords

Unstable critical point
exit problem
fast switching
piecewise deterministic Markov process
small noise

ASJC Scopus subject areas

Modeling and Simulation

Access to Document

10.1142/S0219493720500264

Cite this

@article{78739b5259164fc2a55f0e0112cc6fc5,

title = "Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium",

abstract = "We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus, this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.",

keywords = "Unstable critical point, exit problem, fast switching, piecewise deterministic Markov process, small noise",

author = "Yuri Bakhtin and Alexisz Ga{\'a}l",

note = "Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",

year = "2020",

month = aug,

day = "1",

doi = "10.1142/S0219493720500264",

language = "English (US)",

volume = "20",

journal = "Stochastics and Dynamics",

issn = "0219-4937",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "4",

}

TY - JOUR

T1 - Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

AU - Bakhtin, Yuri

AU - Gaál, Alexisz

PY - 2020/8/1

Y1 - 2020/8/1

N2 - We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus, this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.

AB - We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus, this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.

KW - Unstable critical point

KW - exit problem

KW - fast switching

KW - piecewise deterministic Markov process

KW - small noise

UR - http://www.scopus.com/inward/record.url?scp=85074205414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074205414&partnerID=8YFLogxK

U2 - 10.1142/S0219493720500264

DO - 10.1142/S0219493720500264

M3 - Article

AN - SCOPUS:85074205414

SN - 0219-4937

VL - 20

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

IS - 4

M1 - 2050026

ER -

Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this