Forbidden transitions in Markovian systems
An important result in the theory of Markov chains in continuous time is the Lévy dichotomy, that a transition probability is either always or never zero. This was proved by Ornstein for autonomous chains, in which the transition probabilities are invariant under time shifts, and this paper consider...
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| Veröffentlicht in: | Proceedings of the London Mathematical Society 2012-10, Vol.105 (4), p.730-756 |
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| description | An important result in the theory of Markov chains in continuous time is the Lévy dichotomy, that a transition probability is either always or never zero. This was proved by Ornstein for autonomous chains, in which the transition probabilities are invariant under time shifts, and this paper considers the situation when this invariance is not assumed. The problem was solved for finite chains in joint work with David Williams in 1973, but the case of a countable infinity of states is much deeper. By analysing the family of relations on the state space that codify the zeros of the transition probabilities, it proves possible to develop a general theory that generalizes Ornstein's theorem, though many questions remain open. |
| doi_str_mv | 10.1112/plms/pds021 |
| format | Article |
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F. C.</creator><creatorcontrib>Kingman, J. F. C.</creatorcontrib><description>An important result in the theory of Markov chains in continuous time is the Lévy dichotomy, that a transition probability is either always or never zero. This was proved by Ornstein for autonomous chains, in which the transition probabilities are invariant under time shifts, and this paper considers the situation when this invariance is not assumed. The problem was solved for finite chains in joint work with David Williams in 1973, but the case of a countable infinity of states is much deeper. By analysing the family of relations on the state space that codify the zeros of the transition probabilities, it proves possible to develop a general theory that generalizes Ornstein's theorem, though many questions remain open.</description><identifier>ISSN: 0024-6115</identifier><identifier>EISSN: 1460-244X</identifier><identifier>DOI: 10.1112/plms/pds021</identifier><language>eng</language><publisher>Oxford University Press</publisher><subject>Codification ; Dichotomies ; Forbidden transitions ; Infinity ; Invariants ; Markov processes ; Mathematical analysis ; Transition probabilities</subject><ispartof>Proceedings of the London Mathematical Society, 2012-10, Vol.105 (4), p.730-756</ispartof><rights>2012 London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2Fplms%2Fpds021$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2Fplms%2Fpds021$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Kingman, J. F. C.</creatorcontrib><title>Forbidden transitions in Markovian systems</title><title>Proceedings of the London Mathematical Society</title><description>An important result in the theory of Markov chains in continuous time is the Lévy dichotomy, that a transition probability is either always or never zero. This was proved by Ornstein for autonomous chains, in which the transition probabilities are invariant under time shifts, and this paper considers the situation when this invariance is not assumed. The problem was solved for finite chains in joint work with David Williams in 1973, but the case of a countable infinity of states is much deeper. By analysing the family of relations on the state space that codify the zeros of the transition probabilities, it proves possible to develop a general theory that generalizes Ornstein's theorem, though many questions remain open.</description><subject>Codification</subject><subject>Dichotomies</subject><subject>Forbidden transitions</subject><subject>Infinity</subject><subject>Invariants</subject><subject>Markov processes</subject><subject>Mathematical analysis</subject><subject>Transition probabilities</subject><issn>0024-6115</issn><issn>1460-244X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp90E9LwzAYx_EgCs7pyTfQoyh1eZI0bY4ynAobCip4C2maQLT_zNM59u7tqGdPz-XD74EvIZdAbwGALfq6wUVfIWVwRGYgJE2ZEB_HZEYpE6kEyE7JGeInpVRyns3I9aqLZagq1yZDNC2GIXQtJqFNNiZ-dT_BtAnucXANnpMTb2p0F393Tt5X92_Lx3T9_PC0vFunlsnxoaUSqsJWghdWcSkdU9LluReyKIQtBJSKKe68sKo0nitbMpELn1WGVt7kns_J1bTbx-5763DQTUDr6tq0rtuihixTctxQMNKbidrYIUbndR9DY-JeA9WHIvpQRE9FRg2T3oXa7f-j-mW9eaU5p_wXcqRlNg</recordid><startdate>201210</startdate><enddate>201210</enddate><creator>Kingman, J. F. C.</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201210</creationdate><title>Forbidden transitions in Markovian systems</title><author>Kingman, J. F. C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2660-c061d8cd438c9366e296e77f46884c841b9293ef4c9baf39cb2474f5da0dfa7f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Codification</topic><topic>Dichotomies</topic><topic>Forbidden transitions</topic><topic>Infinity</topic><topic>Invariants</topic><topic>Markov processes</topic><topic>Mathematical analysis</topic><topic>Transition probabilities</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kingman, J. F. 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C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Forbidden transitions in Markovian systems</atitle><jtitle>Proceedings of the London Mathematical Society</jtitle><date>2012-10</date><risdate>2012</risdate><volume>105</volume><issue>4</issue><spage>730</spage><epage>756</epage><pages>730-756</pages><issn>0024-6115</issn><eissn>1460-244X</eissn><abstract>An important result in the theory of Markov chains in continuous time is the Lévy dichotomy, that a transition probability is either always or never zero. This was proved by Ornstein for autonomous chains, in which the transition probabilities are invariant under time shifts, and this paper considers the situation when this invariance is not assumed. The problem was solved for finite chains in joint work with David Williams in 1973, but the case of a countable infinity of states is much deeper. By analysing the family of relations on the state space that codify the zeros of the transition probabilities, it proves possible to develop a general theory that generalizes Ornstein's theorem, though many questions remain open.</abstract><pub>Oxford University Press</pub><doi>10.1112/plms/pds021</doi><tpages>27</tpages></addata></record> |
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| subjects | Codification Dichotomies Forbidden transitions Infinity Invariants Markov processes Mathematical analysis Transition probabilities |
| title | Forbidden transitions in Markovian systems |
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