Markov Chain Models — Rarity and Exponentiality:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1979
|
| Schriftenreihe: | Applied Mathematical Sciences
28 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class |
| Beschreibung: | 1 Online-Ressource (208p) |
| ISBN: | 9781461262008 9780387904054 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-6200-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420457 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1979 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461262008 |c Online |9 978-1-4612-6200-8 | ||
| 020 | |a 9780387904054 |c Print |9 978-0-387-90405-4 | ||
| 024 | 7 | |a 10.1007/978-1-4612-6200-8 |2 doi | |
| 035 | |a (OCoLC)1184369005 | ||
| 035 | |a (DE-599)BVBBV042420457 | ||
| 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 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Keilson, Julian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Markov Chain Models — Rarity and Exponentiality |c edited by Julian Keilson |
| 264 | 1 | |a New York, NY |b Springer New York |c 1979 | |
| 300 | |a 1 Online-Ressource (208p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Applied Mathematical Sciences |v 28 |x 0066-5452 | |
| 500 | |a in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Markov-Modell |0 (DE-588)4168923-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Markov-Prozess |0 (DE-588)4134948-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Markov-Kette |0 (DE-588)4037612-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Markov-Modell |0 (DE-588)4168923-9 |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 | |
| 689 | 2 | 0 | |a Markov-Kette |0 (DE-588)4037612-6 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-6200-8 |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:BVB01-027855874 | ||
| 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 | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153092371906560 |
|---|---|
| any_adam_object | |
| author | Keilson, Julian |
| author_facet | Keilson, Julian |
| author_role | aut |
| author_sort | Keilson, Julian |
| author_variant | j k jk |
| building | Verbundindex |
| bvnumber | BV042420457 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184369005 (DE-599)BVBBV042420457 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-6200-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03245nmm a2200541zcb4500</leader><controlfield tag="001">BV042420457</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1979 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461262008</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-6200-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387904054</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-90405-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-6200-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184369005</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420457</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">510</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">Keilson, Julian</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Markov Chain Models — Rarity and Exponentiality</subfield><subfield code="c">edited by Julian Keilson</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1979</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (208p)</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">Applied Mathematical Sciences</subfield><subfield code="v">28</subfield><subfield code="x">0066-5452</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Markov-Modell</subfield><subfield code="0">(DE-588)4168923-9</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="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="689" ind1="0" ind2="0"><subfield code="a">Markov-Modell</subfield><subfield code="0">(DE-588)4168923-9</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="689" ind1="2" 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="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-6200-8</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:BVB01-027855874</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\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.BV042420457 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461262008 9780387904054 |
| issn | 0066-5452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855874 |
| oclc_num | 1184369005 |
| 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 (208p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Applied Mathematical Sciences |
| spelling | Keilson, Julian Verfasser aut Markov Chain Models — Rarity and Exponentiality edited by Julian Keilson New York, NY Springer New York 1979 1 Online-Ressource (208p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 28 0066-5452 in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class Mathematics Mathematics, general Mathematik Markov-Modell (DE-588)4168923-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Modell (DE-588)4168923-9 s 1\p DE-604 Markov-Prozess (DE-588)4134948-9 s 2\p DE-604 Markov-Kette (DE-588)4037612-6 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-6200-8 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Keilson, Julian Markov Chain Models — Rarity and Exponentiality Mathematics Mathematics, general Mathematik Markov-Modell (DE-588)4168923-9 gnd Markov-Prozess (DE-588)4134948-9 gnd Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4168923-9 (DE-588)4134948-9 (DE-588)4037612-6 |
| title | Markov Chain Models — Rarity and Exponentiality |
| title_auth | Markov Chain Models — Rarity and Exponentiality |
| title_exact_search | Markov Chain Models — Rarity and Exponentiality |
| title_full | Markov Chain Models — Rarity and Exponentiality edited by Julian Keilson |
| title_fullStr | Markov Chain Models — Rarity and Exponentiality edited by Julian Keilson |
| title_full_unstemmed | Markov Chain Models — Rarity and Exponentiality edited by Julian Keilson |
| title_short | Markov Chain Models — Rarity and Exponentiality |
| title_sort | markov chain models rarity and exponentiality |
| topic | Mathematics Mathematics, general Mathematik Markov-Modell (DE-588)4168923-9 gnd Markov-Prozess (DE-588)4134948-9 gnd Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Markov-Modell Markov-Prozess Markov-Kette |
| url | https://doi.org/10.1007/978-1-4612-6200-8 |
| work_keys_str_mv | AT keilsonjulian markovchainmodelsrarityandexponentiality |