Asymptotic analysis of mean exit time for dynamical systems with a single well potential

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Asymptotic analysis of mean exit time for dynamical systems with a single well potential. / Borisov, D.; Sultanov, O.

в: Journal of Differential Equations, Том 269, № 8, 05.10.2020, стр. 78-116.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{7b1839f6d4114f20ad00607b6c0a0c59,

title = "Asymptotic analysis of mean exit time for dynamical systems with a single well potential",

abstract = "We study the mean exit time from a bounded multi-dimensional domain Ω of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (−ε2Δ+∇V⋅∇)uε=1inΩ,uε=0on∂Ω,ε→0. The function V is smooth enough and has the only minimum at the origin contained in Ω; the minimum can be degenerate. At other points of Ω, the gradient of V is non-zero and the normal derivative of V at the boundary ∂Ω does not vanish. Our main result is a complete asymptotic expansion for uε. The asymptotics for uε involves an exponentially large term, which we find in a closed form. We also construct a power in ε asymptotic expansion such that this expansion and a mentioned exponentially large term approximate uε up to arbitrary power of ε.",

keywords = "Asymptotics, Equations with small parameter at higher derivatives, Exit time problem, Overdamped Langevin dynamics",

author = "D. Borisov and O. Sultanov",

year = "2020",

month = oct,

day = "5",

doi = "10.1016/j.jde.2020.04.045",

language = "English",

volume = "269",

pages = "78--116",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Elsevier",

number = "8",

}

RIS

TY - JOUR

T1 - Asymptotic analysis of mean exit time for dynamical systems with a single well potential

AU - Borisov, D.

AU - Sultanov, O.

PY - 2020/10/5

Y1 - 2020/10/5

N2 - We study the mean exit time from a bounded multi-dimensional domain Ω of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (−ε2Δ+∇V⋅∇)uε=1inΩ,uε=0on∂Ω,ε→0. The function V is smooth enough and has the only minimum at the origin contained in Ω; the minimum can be degenerate. At other points of Ω, the gradient of V is non-zero and the normal derivative of V at the boundary ∂Ω does not vanish. Our main result is a complete asymptotic expansion for uε. The asymptotics for uε involves an exponentially large term, which we find in a closed form. We also construct a power in ε asymptotic expansion such that this expansion and a mentioned exponentially large term approximate uε up to arbitrary power of ε.

AB - We study the mean exit time from a bounded multi-dimensional domain Ω of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (−ε2Δ+∇V⋅∇)uε=1inΩ,uε=0on∂Ω,ε→0. The function V is smooth enough and has the only minimum at the origin contained in Ω; the minimum can be degenerate. At other points of Ω, the gradient of V is non-zero and the normal derivative of V at the boundary ∂Ω does not vanish. Our main result is a complete asymptotic expansion for uε. The asymptotics for uε involves an exponentially large term, which we find in a closed form. We also construct a power in ε asymptotic expansion such that this expansion and a mentioned exponentially large term approximate uε up to arbitrary power of ε.

KW - Asymptotics

KW - Equations with small parameter at higher derivatives

KW - Exit time problem

KW - Overdamped Langevin dynamics

UR - http://www.scopus.com/inward/record.url?scp=85084263541&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2020.04.045

DO - 10.1016/j.jde.2020.04.045

M3 - Article

AN - SCOPUS:85084263541

VL - 269

SP - 78

EP - 116

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 8

ER -

ID: 126272906