Loading…
On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity
The limiting behavior of stochastic evolution processes with small noise intensity ϵ is investigated in distribution-based approaches. Let μ ϵ be a stationary measure for stochastic process X ϵ with small ϵ and X 0 be a semiflow on a Polish space. Assume that { μ ϵ : 0 < ϵ ⩽ ϵ 0 } is tight. Then...
Saved in:
| Published in: | Science China. Mathematics 2020-08, Vol.63 (8), p.1463-1504 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3 |
| container_end_page | 1504 |
| container_issue | 8 |
| container_start_page | 1463 |
| container_title | Science China. Mathematics |
| container_volume | 63 |
| creator | Chen, Lifeng Dong, Zhao Jiang, Jifa Zhai, Jianliang |
| description | The limiting behavior of stochastic evolution processes with small noise intensity
ϵ
is investigated in distribution-based approaches. Let
μ
ϵ
be a stationary measure for stochastic process
X
ϵ
with small
ϵ
and
X
0
be a semiflow on a Polish space. Assume that {
μ
ϵ
: 0 <
ϵ
⩽
ϵ
0
} is tight. Then all their limits in the weak sense are
X
0
-invariant and their supports are contained in the Birkhoff center of
X
0
. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, and stochastic functional differential equations driven by Brownian motion or Lévy processes. |
| doi_str_mv | 10.1007/s11425-018-9527-1 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2425623116</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2425623116</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3</originalsourceid><addsrcrecordid>eNp1kE1rwzAMhs3YYGXrD9jNsHM2f8ROchxlX1DoZTsbO7FblyTuLKej_34uGew0HSSB3ldCD0J3lDxQQqpHoLRkoiC0LhrBqoJeoAWtZVPkxC5zL6uyqFjNr9ESYE9y8IaUFV-g7WbEvR988uMWG7vTRx8iDg5D0smHUccTHqyGKVrALo8ghXanIfkW22Pop7MIwwmSHQB_-7TDMOi-x2PwYLEfkx3Bp9MtunK6B7v8rTfo8-X5Y_VWrDev76unddFyKlNhtOssFUaaxhknDC1Fx1vNnTbWlB3XndGaGNtU3AimRWMsF7WxUrhSyM7wG3Q_7z3E8DVZSGofpjjmk4plRpJxSmVW0VnVxgAQrVOH6If8q6JEnZGqGanKSNUZqaLZw2YPZO24tfFv8_-mH5GTfSU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2425623116</pqid></control><display><type>article</type><title>On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity</title><source>Springer Link</source><creator>Chen, Lifeng ; Dong, Zhao ; Jiang, Jifa ; Zhai, Jianliang</creator><creatorcontrib>Chen, Lifeng ; Dong, Zhao ; Jiang, Jifa ; Zhai, Jianliang</creatorcontrib><description>The limiting behavior of stochastic evolution processes with small noise intensity
ϵ
is investigated in distribution-based approaches. Let
μ
ϵ
be a stationary measure for stochastic process
X
ϵ
with small
ϵ
and
X
0
be a semiflow on a Polish space. Assume that {
μ
ϵ
: 0 <
ϵ
⩽
ϵ
0
} is tight. Then all their limits in the weak sense are
X
0
-invariant and their supports are contained in the Birkhoff center of
X
0
. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, and stochastic functional differential equations driven by Brownian motion or Lévy processes.</description><identifier>ISSN: 1674-7283</identifier><identifier>EISSN: 1869-1862</identifier><identifier>DOI: 10.1007/s11425-018-9527-1</identifier><language>eng</language><publisher>Beijing: Science China Press</publisher><subject>Applications of Mathematics ; Brownian motion ; Constraining ; Evolution ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Noise intensity ; Ordinary differential equations ; Partial differential equations ; Stochastic processes</subject><ispartof>Science China. Mathematics, 2020-08, Vol.63 (8), p.1463-1504</ispartof><rights>Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3</citedby><cites>FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Chen, Lifeng</creatorcontrib><creatorcontrib>Dong, Zhao</creatorcontrib><creatorcontrib>Jiang, Jifa</creatorcontrib><creatorcontrib>Zhai, Jianliang</creatorcontrib><title>On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity</title><title>Science China. Mathematics</title><addtitle>Sci. China Math</addtitle><description>The limiting behavior of stochastic evolution processes with small noise intensity
ϵ
is investigated in distribution-based approaches. Let
μ
ϵ
be a stationary measure for stochastic process
X
ϵ
with small
ϵ
and
X
0
be a semiflow on a Polish space. Assume that {
μ
ϵ
: 0 <
ϵ
⩽
ϵ
0
} is tight. Then all their limits in the weak sense are
X
0
-invariant and their supports are contained in the Birkhoff center of
X
0
. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, and stochastic functional differential equations driven by Brownian motion or Lévy processes.</description><subject>Applications of Mathematics</subject><subject>Brownian motion</subject><subject>Constraining</subject><subject>Evolution</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Noise intensity</subject><subject>Ordinary differential equations</subject><subject>Partial differential equations</subject><subject>Stochastic processes</subject><issn>1674-7283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kE1rwzAMhs3YYGXrD9jNsHM2f8ROchxlX1DoZTsbO7FblyTuLKej_34uGew0HSSB3ldCD0J3lDxQQqpHoLRkoiC0LhrBqoJeoAWtZVPkxC5zL6uyqFjNr9ESYE9y8IaUFV-g7WbEvR988uMWG7vTRx8iDg5D0smHUccTHqyGKVrALo8ghXanIfkW22Pop7MIwwmSHQB_-7TDMOi-x2PwYLEfkx3Bp9MtunK6B7v8rTfo8-X5Y_VWrDev76unddFyKlNhtOssFUaaxhknDC1Fx1vNnTbWlB3XndGaGNtU3AimRWMsF7WxUrhSyM7wG3Q_7z3E8DVZSGofpjjmk4plRpJxSmVW0VnVxgAQrVOH6If8q6JEnZGqGanKSNUZqaLZw2YPZO24tfFv8_-mH5GTfSU</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Chen, Lifeng</creator><creator>Dong, Zhao</creator><creator>Jiang, Jifa</creator><creator>Zhai, Jianliang</creator><general>Science China Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200801</creationdate><title>On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity</title><author>Chen, Lifeng ; Dong, Zhao ; Jiang, Jifa ; Zhai, Jianliang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applications of Mathematics</topic><topic>Brownian motion</topic><topic>Constraining</topic><topic>Evolution</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Noise intensity</topic><topic>Ordinary differential equations</topic><topic>Partial differential equations</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Lifeng</creatorcontrib><creatorcontrib>Dong, Zhao</creatorcontrib><creatorcontrib>Jiang, Jifa</creatorcontrib><creatorcontrib>Zhai, Jianliang</creatorcontrib><collection>CrossRef</collection><jtitle>Science China. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Lifeng</au><au>Dong, Zhao</au><au>Jiang, Jifa</au><au>Zhai, Jianliang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity</atitle><jtitle>Science China. Mathematics</jtitle><stitle>Sci. China Math</stitle><date>2020-08-01</date><risdate>2020</risdate><volume>63</volume><issue>8</issue><spage>1463</spage><epage>1504</epage><pages>1463-1504</pages><issn>1674-7283</issn><eissn>1869-1862</eissn><abstract>The limiting behavior of stochastic evolution processes with small noise intensity
ϵ
is investigated in distribution-based approaches. Let
μ
ϵ
be a stationary measure for stochastic process
X
ϵ
with small
ϵ
and
X
0
be a semiflow on a Polish space. Assume that {
μ
ϵ
: 0 <
ϵ
⩽
ϵ
0
} is tight. Then all their limits in the weak sense are
X
0
-invariant and their supports are contained in the Birkhoff center of
X
0
. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, and stochastic functional differential equations driven by Brownian motion or Lévy processes.</abstract><cop>Beijing</cop><pub>Science China Press</pub><doi>10.1007/s11425-018-9527-1</doi><tpages>42</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1674-7283 |
| ispartof | Science China. Mathematics, 2020-08, Vol.63 (8), p.1463-1504 |
| issn | 1674-7283 1869-1862 |
| language | eng |
| recordid | cdi_proquest_journals_2425623116 |
| source | Springer Link |
| subjects | Applications of Mathematics Brownian motion Constraining Evolution Mathematical analysis Mathematics Mathematics and Statistics Noise intensity Ordinary differential equations Partial differential equations Stochastic processes |
| title | On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T16%3A27%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20limiting%20behavior%20of%20stationary%20measures%20for%20stochastic%20evolution%20systems%20with%20small%20noise%20intensity&rft.jtitle=Science%20China.%20Mathematics&rft.au=Chen,%20Lifeng&rft.date=2020-08-01&rft.volume=63&rft.issue=8&rft.spage=1463&rft.epage=1504&rft.pages=1463-1504&rft.issn=1674-7283&rft.eissn=1869-1862&rft_id=info:doi/10.1007/s11425-018-9527-1&rft_dat=%3Cproquest_cross%3E2425623116%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c316t-bafde15b6b9fbf5b145d3ca3fabeb4d3adbaa0be973b52a59be358be65f456db3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2425623116&rft_id=info:pmid/&rfr_iscdi=true |