Ergodic measures of Markov semigroups with the e-property
We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on...
Saved in:
| Published in | Ergodic theory and dynamical systems Vol. 32; no. 3; pp. 1117 - 1135 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.06.2012
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on the set of ergodic measures, one of them being the existence of a Borel subset K0 of K with a bijective map from K0 to the ergodic measures, by sending a point in K0 to the weak limit of the Cesàro averages of the Dirac measure on this point. We also give sufficient conditions for the set of ergodic measures to be countable and finite. Finally, we give a quite general condition under which the Cesàro averages of any measure converge to an invariant measure. |
|---|---|
| AbstractList | We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on the set of ergodic measures, one of them being the existence of a Borel subset K sub(0) of K with a bijective map from K sub(0) to the ergodic measures, by sending a point in K sub(0) to the weak limit of the Cesaro averages of the Dirac measure on this point. We also give sufficient conditions for the set of ergodic measures to be countable and finite. Finally, we give a quite general condition under which the Cesaro averages of any measure converge to an invariant measure. We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on the set of ergodic measures, one of them being the existence of a Borel subset K0 of K with a bijective map from K0 to the ergodic measures, by sending a point in K0 to the weak limit of the Cesàro averages of the Dirac measure on this point. We also give sufficient conditions for the set of ergodic measures to be countable and finite. Finally, we give a quite general condition under which the Cesàro averages of any measure converge to an invariant measure. Abstract We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on the set of ergodic measures, one of them being the existence of a Borel subset K0 of K with a bijective map from K0 to the ergodic measures, by sending a point in K0 to the weak limit of the Cesàro averages of the Dirac measure on this point. We also give sufficient conditions for the set of ergodic measures to be countable and finite. Finally, we give a quite general condition under which the Cesàro averages of any measure converge to an invariant measure. [PUBLICATION ABSTRACT] Abstract We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an equicontinuity condition. We introduce a weak concentrating condition around a compact set K and show that this condition has several implications on the set of ergodic measures, one of them being the existence of a Borel subset K 0 of K with a bijective map from K 0 to the ergodic measures, by sending a point in K 0 to the weak limit of the Cesàro averages of the Dirac measure on this point. We also give sufficient conditions for the set of ergodic measures to be countable and finite. Finally, we give a quite general condition under which the Cesàro averages of any measure converge to an invariant measure. |
| Author | SZAREK, TOMASZ WORM, DANIËL T. H. |
| Author_xml | – sequence: 1 givenname: TOMASZ surname: SZAREK fullname: SZAREK, TOMASZ email: szarek@itl.pl organization: †University of Gdańsk, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland (email: szarek@itl.pl) – sequence: 2 givenname: DANIËL T. H. surname: WORM fullname: WORM, DANIËL T. H. email: daniel.worm@gmail.com organization: ‡Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA Leiden, The Netherlands (email: daniel.worm@gmail.com) |
| BookMark | eNp1kD9PwzAQxS1UJNrCB2CzxMIS8MV2XI-oKn-kIgZgjoxzaVOaONgJqN8eR-2AQNxwN7zfuzu9CRk1rkFCzoFdAQN1_cxAcD6TCoDFStMjMgaR6UQIUCMyHuRk0E_IJIRNRDgoOSZ64VeuqCyt0YTeY6CupI_Gv7tPGrCuVt71baBfVbem3RopJq13Lfpud0qOS7MNeHaYU_J6u3iZ3yfLp7uH-c0ysVyyLsm4YGmWSS1YqRm3qMpCwkyJ1JbAdQaZxBLTInahUzRWCmWksUYyzZADn5LL_d54-KPH0OV1FSxut6ZB14ccpAAhZKoH9OIXunG9b-J3eQyJaa2kVJGCPWW9C8Fjmbe-qo3fRWjgVP4nzOjhB4-p33xVrPDn6v9c3-GBdYU |
| CitedBy_id | crossref_primary_10_1016_j_spa_2017_12_006 crossref_primary_10_1016_j_spl_2020_108964 crossref_primary_10_1007_s10255_023_1072_5 crossref_primary_10_1007_s11118_014_9429_2 crossref_primary_10_1142_S0218202524400037 crossref_primary_10_1080_07362994_2013_836716 crossref_primary_10_1007_s00025_024_02134_2 crossref_primary_10_1016_j_jmaa_2016_11_072 crossref_primary_10_1016_j_crma_2017_10_019 crossref_primary_10_1137_15M1049774 crossref_primary_10_1017_etds_2012_187 |
| Cites_doi | 10.1007/978-1-4612-6371-5 10.1007/s11118-011-9242-0 10.1016/j.jde.2006.04.018 10.1007/s00233-009-9176-7 10.4064/sm-143-2-145-152 10.1112/blms/bdq055 10.1007/s10440-011-9626-6 10.1017/S0143385710000039 10.1239/jap/1158784945 10.4064/sm-27-3-251-268 10.4007/annals.2006.164.993 10.1007/s00020-008-1652-z 10.1007/978-3-540-34514-5 10.1214/09-AOP513 10.1007/978-1-4471-3267-7 10.1007/s002200200639 10.1017/CBO9780511662829 |
| ContentType | Journal Article |
| Copyright | Copyright © Cambridge University Press 2011 |
| Copyright_xml | – notice: Copyright © Cambridge University Press 2011 |
| DBID | AAYXX CITATION 3V. 7SC 7U5 7XB 88I 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ H8D HCIFZ JQ2 K7- L6V L7M L~C L~D M2P M7S P5Z P62 PQEST PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1017/S0143385711000022 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central ProQuest Central Student Aerospace Database SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central Aerospace Database ProQuest Engineering Collection ProQuest Central Korea Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Solid State and Superconductivity Abstracts ProQuest One Academic ProQuest Central (Alumni) |
| DatabaseTitleList | Aerospace Database Computer Science Database CrossRef |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1469-4417 |
| EndPage | 1135 |
| ExternalDocumentID | 2651381261 10_1017_S0143385711000022 |
| Genre | Feature |
| GroupedDBID | --Z -1D -1F -2P -2V -DZ -E. -~6 -~N -~X .FH 09C 09E 0E1 0R~ 29G 3V. 4.4 5GY 5VS 6TJ 6~7 74X 74Y 7~V 88I 8FE 8FG 8R4 8R5 9M5 AAAZR AABES AABWE AACJH AAEED AAGFV AAKTX AAMNQ AANRG AARAB AASVR AAUIS AAUKB ABBXD ABBZL ABITZ ABJCF ABJNI ABKKG ABMWE ABMYL ABQTM ABQWD ABROB ABTCQ ABUWG ABVFV ABXAU ABZCX ACBMC ACCHT ACETC ACGFS ACGOD ACIMK ACIWK ACMRT ACQFJ ACREK ACUIJ ACUYZ ACWGA ACYZP ACZBM ACZUX ACZWT ADCGK ADDNB ADFEC ADGEJ ADKIL ADOCW ADOVH ADOVT ADVJH AEBAK AEBPU AEHGV AEMTW AENCP AENEX AENGE AETEA AEYYC AFFUJ AFKQG AFKRA AFKSM AFLOS AFLVW AFUTZ AGABE AGBYD AGJUD AGLWM AGOOT AHQXX AHRGI AI. AIGNW AIHIV AIOIP AISIE AJ7 AJCYY AJPFC AJQAS AKZCZ ALMA_UNASSIGNED_HOLDINGS ALWZO AQJOH ARABE ARAPS ARZZG ATUCA AUXHV AYIQA AZQEC BBLKV BCGOX BENPR BESQT BGHMG BGLVJ BJBOZ BLZWO BMAJL BPHCQ C0O CAG CBIIA CCPQU CCQAD CCUQV CDIZJ CFAFE CFBFF CGQII CHEAL CJCSC COF CS3 DC4 DOHLZ DU5 DWQXO EBS EGQIC EJD GNUQQ HCIFZ HG- HST HZ~ I.6 I.7 I.9 IH6 IOEEP IOO IS6 I~P J36 J38 J3A JHPGK JQKCU K6V K7- KAFGG KC5 KCGVB KFECR L6V L98 LHUNA LW7 M-V M2P M7S M7~ M8. NIKVX NMFBF NZEOI O9- OYBOY P2P P62 PQQKQ PROAC PTHSS PYCCK Q2X RAMDC RCA RIG ROL RR0 S6- S6U SAAAG T9M TN5 UT1 VH1 WFFJZ WQ3 WXU WXY WYP ZDLDU ZJOSE ZMEZD ZYDXJ ~V1 AAYXX ABVZP CITATION CTKSN 7SC 7U5 7XB 8FD 8FK H8D JQ2 L7M L~C L~D PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c350t-63402665940f903ce7fd518742cf1396165efe2d5ef492eac547a5aca5090e313 |
| IEDL.DBID | 8FG |
| ISSN | 0143-3857 |
| IngestDate | Fri Oct 25 03:01:00 EDT 2024 Thu Oct 10 17:40:07 EDT 2024 Thu Sep 26 17:35:39 EDT 2024 Wed Mar 13 05:56:43 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c350t-63402665940f903ce7fd518742cf1396165efe2d5ef492eac547a5aca5090e313 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1010997557 |
| PQPubID | 36706 |
| PageCount | 19 |
| ParticipantIDs | proquest_miscellaneous_1541445291 proquest_journals_1010997557 crossref_primary_10_1017_S0143385711000022 cambridge_journals_10_1017_S0143385711000022 |
| PublicationCentury | 2000 |
| PublicationDate | 20120600 2012-06-00 20120601 |
| PublicationDateYYYYMMDD | 2012-06-01 |
| PublicationDate_xml | – month: 06 year: 2012 text: 20120600 |
| PublicationDecade | 2010 |
| PublicationPlace | Cambridge, UK |
| PublicationPlace_xml | – name: Cambridge, UK – name: Cambridge |
| PublicationTitle | Ergodic theory and dynamical systems |
| PublicationTitleAlternate | Ergod. Th. Dynam. Sys |
| PublicationYear | 2012 |
| Publisher | Cambridge University Press |
| Publisher_xml | – name: Cambridge University Press |
| References | S0143385711000022_ref3 S0143385711000022_ref2 S0143385711000022_ref5 S0143385711000022_ref4 S0143385711000022_ref1 S0143385711000022_ref11 S0143385711000022_ref12 S0143385711000022_ref10 S0143385711000022_ref7 S0143385711000022_ref6 S0143385711000022_ref9 S0143385711000022_ref8 S0143385711000022_ref19 S0143385711000022_ref17 S0143385711000022_ref18 S0143385711000022_ref15 S0143385711000022_ref16 S0143385711000022_ref13 S0143385711000022_ref14 |
| References_xml | – ident: S0143385711000022_ref19 – ident: S0143385711000022_ref1 doi: 10.1007/978-1-4612-6371-5 – ident: S0143385711000022_ref10 doi: 10.1007/s11118-011-9242-0 – ident: S0143385711000022_ref12 doi: 10.1016/j.jde.2006.04.018 – ident: S0143385711000022_ref9 doi: 10.1007/s00233-009-9176-7 – ident: S0143385711000022_ref15 doi: 10.4064/sm-143-2-145-152 – ident: S0143385711000022_ref16 doi: 10.1112/blms/bdq055 – ident: S0143385711000022_ref18 doi: 10.1007/s10440-011-9626-6 – ident: S0143385711000022_ref17 doi: 10.1017/S0143385710000039 – ident: S0143385711000022_ref3 doi: 10.1239/jap/1158784945 – ident: S0143385711000022_ref5 doi: 10.4064/sm-27-3-251-268 – ident: S0143385711000022_ref6 doi: 10.4007/annals.2006.164.993 – ident: S0143385711000022_ref8 doi: 10.1007/s00020-008-1652-z – ident: S0143385711000022_ref2 doi: 10.1007/978-3-540-34514-5 – ident: S0143385711000022_ref7 – ident: S0143385711000022_ref11 doi: 10.1214/09-AOP513 – ident: S0143385711000022_ref14 doi: 10.1007/978-1-4471-3267-7 – ident: S0143385711000022_ref13 doi: 10.1007/s002200200639 – ident: S0143385711000022_ref4 doi: 10.1017/CBO9780511662829 |
| SSID | ssj0003175 |
| Score | 2.058902 |
| Snippet | We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an... Abstract We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an... Abstract We study the set of ergodic measures for a Markov semigroup on a Polish state space. The principal assumption on this semigroup is the e-property, an... |
| SourceID | proquest crossref cambridge |
| SourceType | Aggregation Database Publisher |
| StartPage | 1117 |
| SubjectTerms | Dynamical systems Ergodic processes Group theory Invariants Markov analysis Markov processes Mathematical analysis |
| Title | Ergodic measures of Markov semigroups with the e-property |
| URI | https://www.cambridge.org/core/product/identifier/S0143385711000022/type/journal_article https://www.proquest.com/docview/1010997557 https://search.proquest.com/docview/1541445291 |
| Volume | 32 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NS8MwFA-6XfQgfuJ0jgiexECbNEl7EpXNIWyIONitpG0CO9jOtRP8783rlw5hlx6SNIeXl_ed90PoJqFeRJUnCZfSOii-K4hSxhDhRVEgAsWjsu3iZCrGM-9lzud1wC2vyyobmVgK6iSLIUZubzfkcCTn8n75SQA1CrKrNYTGLuq6VEpwvvzRcyuJQTdWJYyMMJ_LJqtZtoy2gzDmlgFuwM797a2wqaM2RXSpd0aH6KA2GPFDdcJHaEenx2h_0nZbzU9QMFxZ73IR448q4JfjzGB4hJN94Vx_LMqXGzmGkCu2v2FNlhCCXxXfp2g2Gr4_jUkNiUBixp2CCGb9PSF44DkmcFispUk4wOrR2FhbTriCa6NpYr9eQK1Q5Z5UXAHuQeBo5rIz1EmzVJ8jDPVtsfQNZ9JqKMdRdtbnIpKKGWpd5h66awkS1oydh1VRmAz_0a-HbhuahcuqUca2xf2Gqn-3bk64h67bacvtkMJQqc7Wdg2glkOu2L3YvsUl2rOmDa2KuvqoU6zW-sqaD0U0KHlkgLqPw-nr2w8nEb28 |
| link.rule.ids | 315,783,787,12777,21400,27936,27937,33385,33386,33756,33757,43612,43817 |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07T8MwELagDMCAeIpCASMxISwlcWwnE0KIUqDt1ErdIie1pQ5tStMi8e-5ywsqpC4ZbMfD2b733UfI3djzY0_7igmlwEAJXMm0tpZJP45DGWoR520Xe33ZGfrvIzEqHW5ZmVZZ8cScUY_TBH3k8LoxhqOEUI_zT4aoURhdLSE0tsmOz0FWY6V4-7XmxCgbixRGznggVBXVzFtGwyCOubmDG7Fzf3srrMuodRady532ITkoFUb6VJzwEdkys2Oy36u7rWYnJHxZgHU5Sei0cPhlNLUUi3DSL5qZ6SSv3Mgoulwp_EYNm6MLfrH8PiXD9svgucNKSASWcOEsmeRg70kpQt-xocMTo-xYIKyel1jQ5aQrhbHGG8PXDz1gqsJXWmjEPQgdw11-RhqzdGbOCcX8tkQFVnAFEspxNMwGQsZKc-uBydwkDzVBovJiZ1GRFKaif_RrkvuKZtG8aJSxaXGrourfrasTbpLbehpuO4Yw9MykK1iDqOUYK3YvNm9xQ3Y7g1436r71Py7JHqg5XpHg1SKN5WJlrkCVWMbX-X35ASLjvwQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Ergodic+measures+of+Markov+semigroups+with+the+e-property&rft.jtitle=Ergodic+theory+and+dynamical+systems&rft.au=SZAREK%2C+TOMASZ&rft.au=WORM%2C+DANI%C3%8BL+T.+H.&rft.date=2012-06-01&rft.pub=Cambridge+University+Press&rft.issn=0143-3857&rft.eissn=1469-4417&rft.volume=32&rft.issue=3&rft.spage=1117&rft.epage=1135&rft_id=info:doi/10.1017%2FS0143385711000022&rft.externalDocID=10_1017_S0143385711000022 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0143-3857&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0143-3857&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0143-3857&client=summon |