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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017077" target="_blank" >RIV/62690094:18470/20:50017077 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0022039620302229/pdfft?md5=998bcec5efc4f4e26eb8f35724fd7749&pid=1-s2.0-S0022039620302229-main.pdf" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039620302229/pdfft?md5=998bcec5efc4f4e26eb8f35724fd7749&pid=1-s2.0-S0022039620302229-main.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2020.04.045" target="_blank" >10.1016/j.jde.2020.04.045</a>

Result language

angličtina

Original language name

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

Original language description

We study the mean exit time from a bounded multi-dimensional domain Omega of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (-epsilon(2)Delta + del V . del)u(epsilon) = 1 in Omega, u(epsilon) = 0 on partial derivative Omega, epsilon -&gt; 0. The function Vis smooth enough and has the only minimum at the origin contained in Omega; the minimum can be degenerate. At other points of Omega, the gradient of Vis non-zero and the normal derivative of Vat the boundary partial derivative Omega does not vanish. Our main result is a complete asymptotic expansion for u(epsilon). The asymptotics for u(epsilon) involves an exponentially large term, which we find in a closed form. We also construct a power in epsilon asymptotic expansion such that this expansion and a mentioned exponentially large term approximate u(epsilon) up to arbitrary power of epsilon. (C) 2020 Elsevier Inc. All rights reserved.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of differential equations

ISSN

0022-0396

e-ISSN

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Volume of the periodical

269

Issue of the periodical within the volume

8

Country of publishing house

US - UNITED STATES

Number of pages

39

Pages from-to

78-116

UT code for WoS article

000538395600004

EID of the result in the Scopus database

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