Sofic random processes
For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measur...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Krieger, Wolfgang [verfasserIn] Weiss, Benjamin [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Erschienen: |
De Gruyter ; 2011 |
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| Umfang: |
17 |
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| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Journal für die reine und angewandte Mathematik (Crelles Journal) - 2012(2011), 671 vom: 08. Dez., Seite 31-47 |
| Übergeordnetes Werk: |
volume:2012 ; year:2011 ; number:671 ; day:08 ; month:12 ; pages:31-47 ; extent:17 |
| Links: |
|---|
| DOI / URN: |
10.1515/CRELLE.2011.164 |
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NLEJ246771100 |
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| 520 | |a For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. | ||
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10.1515/CRELLE.2011.164 doi artikel_Grundlieferung.pp (DE-627)NLEJ246771100 DE-627 ger DE-627 rakwb Krieger, Wolfgang verfasserin aut Sofic random processes De Gruyter 2011 17 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. Walter de Gruyter Online Zeitschriften Weiss, Benjamin verfasserin aut Enthalten in Journal für die reine und angewandte Mathematik (Crelles Journal) 2012(2011), 671 vom: 08. Dez., Seite 31-47 (DE-627)NLEJ24823532X (DE-600)1468592-9 1435-5345 nnns volume:2012 year:2011 number:671 day:08 month:12 pages:31-47 extent:17 https://doi.org/10.1515/CRELLE.2011.164 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 2012 2011 671 08 12 31-47 17 |
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10.1515/CRELLE.2011.164 doi artikel_Grundlieferung.pp (DE-627)NLEJ246771100 DE-627 ger DE-627 rakwb Krieger, Wolfgang verfasserin aut Sofic random processes De Gruyter 2011 17 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. Walter de Gruyter Online Zeitschriften Weiss, Benjamin verfasserin aut Enthalten in Journal für die reine und angewandte Mathematik (Crelles Journal) 2012(2011), 671 vom: 08. Dez., Seite 31-47 (DE-627)NLEJ24823532X (DE-600)1468592-9 1435-5345 nnns volume:2012 year:2011 number:671 day:08 month:12 pages:31-47 extent:17 https://doi.org/10.1515/CRELLE.2011.164 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 2012 2011 671 08 12 31-47 17 |
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10.1515/CRELLE.2011.164 doi artikel_Grundlieferung.pp (DE-627)NLEJ246771100 DE-627 ger DE-627 rakwb Krieger, Wolfgang verfasserin aut Sofic random processes De Gruyter 2011 17 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. Walter de Gruyter Online Zeitschriften Weiss, Benjamin verfasserin aut Enthalten in Journal für die reine und angewandte Mathematik (Crelles Journal) 2012(2011), 671 vom: 08. Dez., Seite 31-47 (DE-627)NLEJ24823532X (DE-600)1468592-9 1435-5345 nnns volume:2012 year:2011 number:671 day:08 month:12 pages:31-47 extent:17 https://doi.org/10.1515/CRELLE.2011.164 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 2012 2011 671 08 12 31-47 17 |
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10.1515/CRELLE.2011.164 doi artikel_Grundlieferung.pp (DE-627)NLEJ246771100 DE-627 ger DE-627 rakwb Krieger, Wolfgang verfasserin aut Sofic random processes De Gruyter 2011 17 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. Walter de Gruyter Online Zeitschriften Weiss, Benjamin verfasserin aut Enthalten in Journal für die reine und angewandte Mathematik (Crelles Journal) 2012(2011), 671 vom: 08. Dez., Seite 31-47 (DE-627)NLEJ24823532X (DE-600)1468592-9 1435-5345 nnns volume:2012 year:2011 number:671 day:08 month:12 pages:31-47 extent:17 https://doi.org/10.1515/CRELLE.2011.164 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 2012 2011 671 08 12 31-47 17 |
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For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. |
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For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. |
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For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ246771100</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820024214.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2011 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/CRELLE.2011.164</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ246771100</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krieger, Wolfgang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sofic random processes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">De Gruyter</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">17</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Weiss, Benjamin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal für die reine und angewandte Mathematik (Crelles Journal)</subfield><subfield code="g">2012(2011), 671 vom: 08. Dez., Seite 31-47</subfield><subfield code="w">(DE-627)NLEJ24823532X</subfield><subfield code="w">(DE-600)1468592-9</subfield><subfield code="x">1435-5345</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2012</subfield><subfield code="g">year:2011</subfield><subfield code="g">number:671</subfield><subfield code="g">day:08</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:31-47</subfield><subfield code="g">extent:17</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/CRELLE.2011.164</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2012</subfield><subfield code="j">2011</subfield><subfield code="e">671</subfield><subfield code="b">08</subfield><subfield code="c">12</subfield><subfield code="h">31-47</subfield><subfield code="g">17</subfield></datafield></record></collection>
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