Markov Chains with Stationary Transition Probabilities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1960
|
| Schriftenreihe: | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete
104 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools |
| Beschreibung: | 1 Online-Ressource (X, 278 p) |
| ISBN: | 9783642496868 9783642494086 |
| DOI: | 10.1007/978-3-642-49686-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422546 | ||
| 003 | DE-604 | ||
| 005 | 20190313 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1960 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642496868 |c Online |9 978-3-642-49686-8 | ||
| 020 | |a 9783642494086 |c Print |9 978-3-642-49408-6 | ||
| 024 | 7 | |a 10.1007/978-3-642-49686-8 |2 doi | |
| 035 | |a (OCoLC)863911944 | ||
| 035 | |a (DE-599)BVBBV042422546 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 540 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Chung, Kai Lai |d 1917-2009 |e Verfasser |0 (DE-588)136125484 |4 aut | |
| 245 | 1 | 0 | |a Markov Chains with Stationary Transition Probabilities |c by Kai Lai Chung |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1960 | |
| 300 | |a 1 Online-Ressource (X, 278 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete |v 104 | |
| 500 | |a The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools | ||
| 650 | 4 | |a Chemistry | |
| 650 | 4 | |a Chemistry/Food Science, general | |
| 650 | 4 | |a Chemie | |
| 650 | 0 | 7 | |a Stationärer Prozess |0 (DE-588)4056989-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Markov-Kette |0 (DE-588)4037612-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Markov-Prozess |0 (DE-588)4134948-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Markov-Kette |0 (DE-588)4037612-6 |D s |
| 689 | 0 | 1 | |a Stationärer Prozess |0 (DE-588)4056989-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Markov-Prozess |0 (DE-588)4134948-9 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-49686-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857963 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153097145024512 |
|---|---|
| any_adam_object | |
| author | Chung, Kai Lai 1917-2009 |
| author_GND | (DE-588)136125484 |
| author_facet | Chung, Kai Lai 1917-2009 |
| author_role | aut |
| author_sort | Chung, Kai Lai 1917-2009 |
| author_variant | k l c kl klc |
| building | Verbundindex |
| bvnumber | BV042422546 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863911944 (DE-599)BVBBV042422546 |
| dewey-full | 540 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 540 - Chemistry and allied sciences |
| dewey-raw | 540 |
| dewey-search | 540 |
| dewey-sort | 3540 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Mathematik |
| doi_str_mv | 10.1007/978-3-642-49686-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03456nmm a2200517zcb4500</leader><controlfield tag="001">BV042422546</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190313 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1960 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642496868</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-49686-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642494086</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-49408-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-49686-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863911944</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422546</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">540</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chung, Kai Lai</subfield><subfield code="d">1917-2009</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)136125484</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Markov Chains with Stationary Transition Probabilities</subfield><subfield code="c">by Kai Lai Chung</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1960</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 278 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete</subfield><subfield code="v">104</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chemistry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chemistry/Food Science, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chemie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stationärer Prozess</subfield><subfield code="0">(DE-588)4056989-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Markov-Kette</subfield><subfield code="0">(DE-588)4037612-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Markov-Prozess</subfield><subfield code="0">(DE-588)4134948-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Markov-Kette</subfield><subfield code="0">(DE-588)4037612-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stationärer Prozess</subfield><subfield code="0">(DE-588)4056989-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Markov-Prozess</subfield><subfield code="0">(DE-588)4134948-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-49686-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857963</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042422546 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642496868 9783642494086 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857963 |
| oclc_num | 863911944 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 278 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1960 |
| publishDateSearch | 1960 |
| publishDateSort | 1960 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Chung, Kai Lai 1917-2009 Verfasser (DE-588)136125484 aut Markov Chains with Stationary Transition Probabilities by Kai Lai Chung Berlin, Heidelberg Springer Berlin Heidelberg 1960 1 Online-Ressource (X, 278 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete 104 The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools Chemistry Chemistry/Food Science, general Chemie Stationärer Prozess (DE-588)4056989-5 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s Stationärer Prozess (DE-588)4056989-5 s 1\p DE-604 Markov-Prozess (DE-588)4134948-9 s 2\p DE-604 https://doi.org/10.1007/978-3-642-49686-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chung, Kai Lai 1917-2009 Markov Chains with Stationary Transition Probabilities Chemistry Chemistry/Food Science, general Chemie Stationärer Prozess (DE-588)4056989-5 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4056989-5 (DE-588)4037612-6 (DE-588)4134948-9 |
| title | Markov Chains with Stationary Transition Probabilities |
| title_auth | Markov Chains with Stationary Transition Probabilities |
| title_exact_search | Markov Chains with Stationary Transition Probabilities |
| title_full | Markov Chains with Stationary Transition Probabilities by Kai Lai Chung |
| title_fullStr | Markov Chains with Stationary Transition Probabilities by Kai Lai Chung |
| title_full_unstemmed | Markov Chains with Stationary Transition Probabilities by Kai Lai Chung |
| title_short | Markov Chains with Stationary Transition Probabilities |
| title_sort | markov chains with stationary transition probabilities |
| topic | Chemistry Chemistry/Food Science, general Chemie Stationärer Prozess (DE-588)4056989-5 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Chemistry Chemistry/Food Science, general Chemie Stationärer Prozess Markov-Kette Markov-Prozess |
| url | https://doi.org/10.1007/978-3-642-49686-8 |
| work_keys_str_mv | AT chungkailai markovchainswithstationarytransitionprobabilities |