Alternative characterization of ergodicity for doubly stochastic chains
In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce an...
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Tagungsbericht |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 5376 |
---|---|
container_issue | |
container_start_page | 5371 |
container_title | |
container_volume | |
creator | Touri, B. Nedic, A. |
description | In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce and study. We then focus on doubly stochastic chains for which we prove that the absolute infinite flow property and ergodicity are equivalent. The proof of this result makes use of a special decomposition of a doubly stochastic matrix, as given by Birkhoff-von Neumann theorem. Finally, we show that a backward product of doubly stochastic matrices is convergent up to a permutation sequence and, as a result, the set of accumulation points of such a product is finite. |
doi_str_mv | 10.1109/CDC.2011.6161372 |
format | Conference Proceeding |
fullrecord | <record><control><sourceid>ieee_6IE</sourceid><recordid>TN_cdi_ieee_primary_6161372</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>6161372</ieee_id><sourcerecordid>6161372</sourcerecordid><originalsourceid>FETCH-LOGICAL-i217t-b451184f0e44da8b7ee4b91176948f48f7062af233c13dda16ceaf0ef072c3b43</originalsourceid><addsrcrecordid>eNotUM9LwzAUjqjgNncXvPQfaH0vyZL0OKpOYeBFzyNNE43URpIo1L_eiIMHH9_PwyPkCqFBhPamu-0aCoiNQIFM0hOyRC4kA76R7JSsW6mKQRVXAOKMLABbrClFcUGWKb0DgAIhFmS3HbONk87-21bmTUdtCvc_RQhTFVxl42sYvPF5rlyI1RC--nGuUg4lnLI3fyU_pUty7vSY7PqIK_Jyf_fcPdT7p91jt93XnqLMdc83iIo7sJwPWvXSWt63iFK0XLlyEgTVjjJmkA2DRmGsLmkHkhrWc7Yi1_-73lp7-Iz-Q8f5cHwC-wXI0k7M</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype></control><display><type>conference_proceeding</type><title>Alternative characterization of ergodicity for doubly stochastic chains</title><source>IEEE Electronic Library (IEL) Conference Proceedings</source><creator>Touri, B. ; Nedic, A.</creator><creatorcontrib>Touri, B. ; Nedic, A.</creatorcontrib><description>In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce and study. We then focus on doubly stochastic chains for which we prove that the absolute infinite flow property and ergodicity are equivalent. The proof of this result makes use of a special decomposition of a doubly stochastic matrix, as given by Birkhoff-von Neumann theorem. Finally, we show that a backward product of doubly stochastic matrices is convergent up to a permutation sequence and, as a result, the set of accumulation points of such a product is finite.</description><identifier>ISSN: 0191-2216</identifier><identifier>ISBN: 9781612848006</identifier><identifier>ISBN: 1612848001</identifier><identifier>EISBN: 1467304573</identifier><identifier>EISBN: 1612847994</identifier><identifier>EISBN: 9781612847993</identifier><identifier>EISBN: 161284801X</identifier><identifier>EISBN: 9781612848013</identifier><identifier>EISBN: 9781467304573</identifier><identifier>DOI: 10.1109/CDC.2011.6161372</identifier><language>eng</language><publisher>IEEE</publisher><subject>Concrete ; Markov processes ; Matrix decomposition ; Nonhomogeneous media ; Trajectory ; Vectors</subject><ispartof>2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, p.5371-5376</ispartof><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6161372$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,780,784,789,790,2058,27925,54920</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6161372$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Touri, B.</creatorcontrib><creatorcontrib>Nedic, A.</creatorcontrib><title>Alternative characterization of ergodicity for doubly stochastic chains</title><title>2011 50th IEEE Conference on Decision and Control and European Control Conference</title><addtitle>CDC</addtitle><description>In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce and study. We then focus on doubly stochastic chains for which we prove that the absolute infinite flow property and ergodicity are equivalent. The proof of this result makes use of a special decomposition of a doubly stochastic matrix, as given by Birkhoff-von Neumann theorem. Finally, we show that a backward product of doubly stochastic matrices is convergent up to a permutation sequence and, as a result, the set of accumulation points of such a product is finite.</description><subject>Concrete</subject><subject>Markov processes</subject><subject>Matrix decomposition</subject><subject>Nonhomogeneous media</subject><subject>Trajectory</subject><subject>Vectors</subject><issn>0191-2216</issn><isbn>9781612848006</isbn><isbn>1612848001</isbn><isbn>1467304573</isbn><isbn>1612847994</isbn><isbn>9781612847993</isbn><isbn>161284801X</isbn><isbn>9781612848013</isbn><isbn>9781467304573</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2011</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNotUM9LwzAUjqjgNncXvPQfaH0vyZL0OKpOYeBFzyNNE43URpIo1L_eiIMHH9_PwyPkCqFBhPamu-0aCoiNQIFM0hOyRC4kA76R7JSsW6mKQRVXAOKMLABbrClFcUGWKb0DgAIhFmS3HbONk87-21bmTUdtCvc_RQhTFVxl42sYvPF5rlyI1RC--nGuUg4lnLI3fyU_pUty7vSY7PqIK_Jyf_fcPdT7p91jt93XnqLMdc83iIo7sJwPWvXSWt63iFK0XLlyEgTVjjJmkA2DRmGsLmkHkhrWc7Yi1_-73lp7-Iz-Q8f5cHwC-wXI0k7M</recordid><startdate>201112</startdate><enddate>201112</enddate><creator>Touri, B.</creator><creator>Nedic, A.</creator><general>IEEE</general><scope>6IE</scope><scope>6IH</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIO</scope></search><sort><creationdate>201112</creationdate><title>Alternative characterization of ergodicity for doubly stochastic chains</title><author>Touri, B. ; Nedic, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i217t-b451184f0e44da8b7ee4b91176948f48f7062af233c13dda16ceaf0ef072c3b43</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Concrete</topic><topic>Markov processes</topic><topic>Matrix decomposition</topic><topic>Nonhomogeneous media</topic><topic>Trajectory</topic><topic>Vectors</topic><toplevel>online_resources</toplevel><creatorcontrib>Touri, B.</creatorcontrib><creatorcontrib>Nedic, A.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Touri, B.</au><au>Nedic, A.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Alternative characterization of ergodicity for doubly stochastic chains</atitle><btitle>2011 50th IEEE Conference on Decision and Control and European Control Conference</btitle><stitle>CDC</stitle><date>2011-12</date><risdate>2011</risdate><spage>5371</spage><epage>5376</epage><pages>5371-5376</pages><issn>0191-2216</issn><isbn>9781612848006</isbn><isbn>1612848001</isbn><eisbn>1467304573</eisbn><eisbn>1612847994</eisbn><eisbn>9781612847993</eisbn><eisbn>161284801X</eisbn><eisbn>9781612848013</eisbn><eisbn>9781467304573</eisbn><abstract>In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce and study. We then focus on doubly stochastic chains for which we prove that the absolute infinite flow property and ergodicity are equivalent. The proof of this result makes use of a special decomposition of a doubly stochastic matrix, as given by Birkhoff-von Neumann theorem. Finally, we show that a backward product of doubly stochastic matrices is convergent up to a permutation sequence and, as a result, the set of accumulation points of such a product is finite.</abstract><pub>IEEE</pub><doi>10.1109/CDC.2011.6161372</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
fulltext | fulltext_linktorsrc |
identifier | ISSN: 0191-2216 |
ispartof | 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, p.5371-5376 |
issn | 0191-2216 |
language | eng |
recordid | cdi_ieee_primary_6161372 |
source | IEEE Electronic Library (IEL) Conference Proceedings |
subjects | Concrete Markov processes Matrix decomposition Nonhomogeneous media Trajectory Vectors |
title | Alternative characterization of ergodicity for doubly stochastic chains |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T18%3A17%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ieee_6IE&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=Alternative%20characterization%20of%20ergodicity%20for%20doubly%20stochastic%20chains&rft.btitle=2011%2050th%20IEEE%20Conference%20on%20Decision%20and%20Control%20and%20European%20Control%20Conference&rft.au=Touri,%20B.&rft.date=2011-12&rft.spage=5371&rft.epage=5376&rft.pages=5371-5376&rft.issn=0191-2216&rft.isbn=9781612848006&rft.isbn_list=1612848001&rft_id=info:doi/10.1109/CDC.2011.6161372&rft_dat=%3Cieee_6IE%3E6161372%3C/ieee_6IE%3E%3Curl%3E%3C/url%3E&rft.eisbn=1467304573&rft.eisbn_list=1612847994&rft.eisbn_list=9781612847993&rft.eisbn_list=161284801X&rft.eisbn_list=9781612848013&rft.eisbn_list=9781467304573&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=6161372&rfr_iscdi=true |