No Cover Image

Journal article 1006 views

An ergodic theorem of a parabolic Anderson model driven by Lévy noise

Yong Liu, Jianglun Wu, Fengxia Yang, Jianliang Zhai, Jiang-lun Wu

Frontiers of Mathematics in China, Volume: 6, Issue: 6, Pages: 1147 - 1183

Swansea University Author: Jiang-lun Wu

Full text not available from this repository: check for access using links below.

Check full text

DOI (Published version): 10.1007/s11464-011-0124-y

Abstract

In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j))i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded nonnegati...

Full description

Published in: Frontiers of Mathematics in China
ISSN: 1673-3452 1673-3576
Published: Berlin, Heidelberg Higher Education Press and Springer-Verlag 2011
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa8021
first_indexed 2017-10-04T18:21:33Z
last_indexed 2018-02-09T04:36:49Z
id cronfa8021
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2017-11-21T16:55:33.4950298</datestamp><bib-version>v2</bib-version><id>8021</id><entry>2012-02-22</entry><title>An ergodic theorem of a parabolic Anderson model driven by L&#xE9;vy noise</title><swanseaauthors><author><sid>dbd67e30d59b0f32592b15b5705af885</sid><firstname>Jiang-lun</firstname><surname>Wu</surname><name>Jiang-lun Wu</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2012-02-22</date><abstract>In this paper, we study an ergodic theorem of a parabolic Andersen model driven by L&#xE9;vy noise. Under the assumption that A = (a(i, j))i,j&#x2208;S is symmetric with respect to a &#x3C3;-finite measure gp, we obtain the long-time convergence to an invariant probability measure &#x3BD;h starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by L&#xE9;vy noise, which is an extension of the result of Y. Liu and F. X. Yang.</abstract><type>Journal Article</type><journal>Frontiers of Mathematics in China</journal><volume>6</volume><journalNumber>6</journalNumber><paginationStart>1147</paginationStart><paginationEnd>1183</paginationEnd><publisher>Higher Education Press and Springer-Verlag</publisher><placeOfPublication>Berlin, Heidelberg</placeOfPublication><issnPrint>1673-3452</issnPrint><issnElectronic>1673-3576</issnElectronic><keywords>Parabolic Anderson model, ergodic theorem, invariant measure, L&#xE9;vy noise, self-duality.</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2011</publishedYear><publishedDate>2011-12-31</publishedDate><doi>10.1007/s11464-011-0124-y</doi><url>https://link.springer.com/content/pdf/10.1007%2Fs11464-011-0124-y.pdf</url><notes></notes><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm/><lastEdited>2017-11-21T16:55:33.4950298</lastEdited><Created>2012-02-22T13:37:04.0000000</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Yong</firstname><surname>Liu</surname><order>1</order></author><author><firstname>Jianglun</firstname><surname>Wu</surname><order>2</order></author><author><firstname>Fengxia</firstname><surname>Yang</surname><order>3</order></author><author><firstname>Jianliang</firstname><surname>Zhai</surname><order>4</order></author><author><firstname>Jiang-lun</firstname><surname>Wu</surname><order>5</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling 2017-11-21T16:55:33.4950298 v2 8021 2012-02-22 An ergodic theorem of a parabolic Anderson model driven by Lévy noise dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2012-02-22 In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j))i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by Lévy noise, which is an extension of the result of Y. Liu and F. X. Yang. Journal Article Frontiers of Mathematics in China 6 6 1147 1183 Higher Education Press and Springer-Verlag Berlin, Heidelberg 1673-3452 1673-3576 Parabolic Anderson model, ergodic theorem, invariant measure, Lévy noise, self-duality. 31 12 2011 2011-12-31 10.1007/s11464-011-0124-y https://link.springer.com/content/pdf/10.1007%2Fs11464-011-0124-y.pdf COLLEGE NANME COLLEGE CODE Swansea University 2017-11-21T16:55:33.4950298 2012-02-22T13:37:04.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Yong Liu 1 Jianglun Wu 2 Fengxia Yang 3 Jianliang Zhai 4 Jiang-lun Wu 5
title An ergodic theorem of a parabolic Anderson model driven by Lévy noise
spellingShingle An ergodic theorem of a parabolic Anderson model driven by Lévy noise
Jiang-lun Wu
title_short An ergodic theorem of a parabolic Anderson model driven by Lévy noise
title_full An ergodic theorem of a parabolic Anderson model driven by Lévy noise
title_fullStr An ergodic theorem of a parabolic Anderson model driven by Lévy noise
title_full_unstemmed An ergodic theorem of a parabolic Anderson model driven by Lévy noise
title_sort An ergodic theorem of a parabolic Anderson model driven by Lévy noise
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Yong Liu
Jianglun Wu
Fengxia Yang
Jianliang Zhai
Jiang-lun Wu
format Journal article
container_title Frontiers of Mathematics in China
container_volume 6
container_issue 6
container_start_page 1147
publishDate 2011
institution Swansea University
issn 1673-3452
1673-3576
doi_str_mv 10.1007/s11464-011-0124-y
publisher Higher Education Press and Springer-Verlag
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url https://link.springer.com/content/pdf/10.1007%2Fs11464-011-0124-y.pdf
document_store_str 0
active_str 0
description In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j))i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by Lévy noise, which is an extension of the result of Y. Liu and F. X. Yang.
published_date 2011-12-31T18:16:09Z
_version_ 1821339780168810496
score 11.04748

Similar Items