Markov chains:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | Reprinted |
| Schriftenreihe: | Cambridge series on statistical and probabilistic mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVI, 237 S. graph. Darst. |
| ISBN: | 9780521481816 9780521633963 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV023041383 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 071210s2007 d||| |||| 00||| eng d | ||
| 020 | |a 9780521481816 |9 978-0-521-48181-6 | ||
| 020 | |a 9780521633963 |9 978-0-521-63396-3 | ||
| 035 | |a (OCoLC)254178997 | ||
| 035 | |a (DE-599)BVBBV023041383 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-M347 |a DE-29T | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a MAT 607f |2 stub | ||
| 100 | 1 | |a Norris, James R. |d 1960- |e Verfasser |0 (DE-588)143186914 |4 aut | |
| 245 | 1 | 0 | |a Markov chains |c J. R. Norris |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XVI, 237 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge series on statistical and probabilistic mathematics |v 2 | |
| 650 | 0 | 7 | |a Markov-Kette |0 (DE-588)4037612-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Markov-Kette |0 (DE-588)4037612-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Cambridge series on statistical and probabilistic mathematics |v 2 |w (DE-604)BV011442366 |9 2 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016244912 | ||
Datensatz im Suchindex
| _version_ | 1804137270069952512 |
|---|---|
| adam_text | Contents
Preface
ix
Introduction
xiii
1.
Discrete-time Markov chains
1
1.1
Definition and basic properties
1
1.2
Class structure
10
1.3
Hitting times and absorption probabilities
12
1.4
Strong Markov property
19
1.5
Recurrence and transience
24
1.6
Recurrence and transience of random walks
29
1.7
Invariant distributions
33
1.8
Convergence to equilibrium
40
1.9
Time reversal
47
1.10
Ergodic theorem
52
1.11
Appendix: recurrence relations
57
1.12
Appendix: asymptotics for n!
58
2.
Continuous-time Markov chains I
60
2.1
Q-matrices and their exponentials
60
2.2
Continuous-time random processes
67
2.3
Some properties of the exponential distribution
70
2.4
Poisson
processes
73
2.5
Birth processes
81
2.6
Jump chain and holding times
87
2.7
Explosion
90
2.8
Forward and backward equations
93
2.9
Non-minimal chains
103
2.10
Appendix: matrix exponentials
105
3.
Continuous-time Markov chains II
108
3.1
Basic properties
108
3.2
Class structure 111
3.3
Hitting times and absorption probabilities
112
3.4
Recurrence and transience
114
3.5
Invariant distributions
117
3.6
Convergence to equilibrium
121
3.7
Time reversal
123
3.8
Ergodic theorem
125
4.
Further theory
128
4.1
Martingales
128
4.2
Potential theory
134
4.3
Electrical networks
151
4.4
Brownian motion
159
5.
Applications
170
5.1
Markov chains in biology
170
5.2
Queues and queueing networks
179
5.3
Markov chains in resource management
192
5.4
Markov decision processes
197
5.5
Markov chain Monte Carlo
206
6.
Appendix: probability and measure
217
6.1
Countable sets and countable sums
217
6.2
Basic facts of measure theory
220
6.3
Probability spaces and expectation
222
6.4
Monotone convergence and Fubini s theorem
223
6.5
Stopping times and the strong Markov property
224
6.6
Uniqueness of probabilities and independence of
σ
-algebras
228
Further reading
232
Index
234
Markov chains are central to the understanding of random processes. This is
not only because they pervade applications, but also because one can calcu¬
late explicitly many quantities of interest. This textbook, aimed at advanced
undergraduate or MSc students with some background in basic probability the¬
ory, focusses on Markov chains and develops quickly a coherent and rigorous
theory. In a non-technical way, it explains methods of calculation for transition
probabilities, hitting probabilities, long-run averages and equilibrium probabilities.
The author presents both discrete-time and continuous-time chains and also
discusses reversibility. He uses random walks as important examples, as well
as
Poisson
processes and birth-and-death processes. A distinguishing feature
of the book is an introduction to more advanced topics such as martingales and
potentials, in the established context of Markov chains. There are applications
to simulation, economics, optimal control, genetics, queues and many other topics.
There is a careful selection of exercises and examples drawn both from theory
and practice. The book will therefore be an ideal text either for elementary
courses on random processes or those that are more oriented towards applications.
|
| adam_txt |
Contents
Preface
ix
Introduction
xiii
1.
Discrete-time Markov chains
1
1.1
Definition and basic properties
1
1.2
Class structure
10
1.3
Hitting times and absorption probabilities
12
1.4
Strong Markov property
19
1.5
Recurrence and transience
24
1.6
Recurrence and transience of random walks
29
1.7
Invariant distributions
33
1.8
Convergence to equilibrium
40
1.9
Time reversal
47
1.10
Ergodic theorem
52
1.11
Appendix: recurrence relations
57
1.12
Appendix: asymptotics for n!
58
2.
Continuous-time Markov chains I
60
2.1
Q-matrices and their exponentials
60
2.2
Continuous-time random processes
67
2.3
Some properties of the exponential distribution
70
2.4
Poisson
processes
73
2.5
Birth processes
81
2.6
Jump chain and holding times
87
2.7
Explosion
90
2.8
Forward and backward equations
93
2.9
Non-minimal chains
103
2.10
Appendix: matrix exponentials
105
3.
Continuous-time Markov chains II
108
3.1
Basic properties
108
3.2
Class structure 111
3.3
Hitting times and absorption probabilities
112
3.4
Recurrence and transience
114
3.5
Invariant distributions
117
3.6
Convergence to equilibrium
121
3.7
Time reversal
123
3.8
Ergodic theorem
125
4.
Further theory
128
4.1
Martingales
128
4.2
Potential theory
134
4.3
Electrical networks
151
4.4
Brownian motion
159
5.
Applications
170
5.1
Markov chains in biology
170
5.2
Queues and queueing networks
179
5.3
Markov chains in resource management
192
5.4
Markov decision processes
197
5.5
Markov chain Monte Carlo
206
6.
Appendix: probability and measure
217
6.1
Countable sets and countable sums
217
6.2
Basic facts of measure theory
220
6.3
Probability spaces and expectation
222
6.4
Monotone convergence and Fubini's theorem
223
6.5
Stopping times and the strong Markov property
224
6.6
Uniqueness of probabilities and independence of
σ
-algebras
228
Further reading
232
Index
234
Markov chains are central to the understanding of random processes. This is
not only because they pervade applications, but also because one can calcu¬
late explicitly many quantities of interest. This textbook, aimed at advanced
undergraduate or MSc students with some background in basic probability the¬
ory, focusses on Markov chains and develops quickly a coherent and rigorous
theory. In a non-technical way, it explains methods of calculation for transition
probabilities, hitting probabilities, long-run averages and equilibrium probabilities.
The author presents both discrete-time and continuous-time chains and also
discusses reversibility. He uses random walks as important examples, as well
as
Poisson
processes and birth-and-death processes. A distinguishing feature
of the book is an introduction to more advanced topics such as martingales and
potentials, in the established context of Markov chains. There are applications
to simulation, economics, optimal control, genetics, queues and many other topics.
There is a careful selection of exercises and examples drawn both from theory
and practice. The book will therefore be an ideal text either for elementary
courses on random processes or those that are more oriented towards applications. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Norris, James R. 1960- |
| author_GND | (DE-588)143186914 |
| author_facet | Norris, James R. 1960- |
| author_role | aut |
| author_sort | Norris, James R. 1960- |
| author_variant | j r n jr jrn |
| building | Verbundindex |
| bvnumber | BV023041383 |
| classification_rvk | SK 820 |
| classification_tum | MAT 607f |
| ctrlnum | (OCoLC)254178997 (DE-599)BVBBV023041383 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprinted |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01721nam a2200385 cb4500</leader><controlfield tag="001">BV023041383</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">071210s2007 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521481816</subfield><subfield code="9">978-0-521-48181-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521633963</subfield><subfield code="9">978-0-521-63396-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)254178997</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023041383</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-M347</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 607f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Norris, James R.</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)143186914</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Markov chains</subfield><subfield code="c">J. R. Norris</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Reprinted</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 237 S.</subfield><subfield code="b">graph. Darst.</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge series on statistical and probabilistic mathematics</subfield><subfield code="v">2</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-Kette</subfield><subfield code="0">(DE-588)4037612-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge series on statistical and probabilistic mathematics</subfield><subfield code="v">2</subfield><subfield code="w">(DE-604)BV011442366</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016244912</subfield></datafield></record></collection> |
| id | DE-604.BV023041383 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:20:45Z |
| indexdate | 2024-07-09T21:09:37Z |
| institution | BVB |
| isbn | 9780521481816 9780521633963 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016244912 |
| oclc_num | 254178997 |
| open_access_boolean | |
| owner | DE-739 DE-M347 DE-29T |
| owner_facet | DE-739 DE-M347 DE-29T |
| physical | XVI, 237 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge series on statistical and probabilistic mathematics |
| series2 | Cambridge series on statistical and probabilistic mathematics |
| spelling | Norris, James R. 1960- Verfasser (DE-588)143186914 aut Markov chains J. R. Norris Reprinted Cambridge [u.a.] Cambridge Univ. Press 2007 XVI, 237 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series on statistical and probabilistic mathematics 2 Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s DE-604 Cambridge series on statistical and probabilistic mathematics 2 (DE-604)BV011442366 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Norris, James R. 1960- Markov chains Cambridge series on statistical and probabilistic mathematics Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4037612-6 |
| title | Markov chains |
| title_auth | Markov chains |
| title_exact_search | Markov chains |
| title_exact_search_txtP | Markov chains |
| title_full | Markov chains J. R. Norris |
| title_fullStr | Markov chains J. R. Norris |
| title_full_unstemmed | Markov chains J. R. Norris |
| title_short | Markov chains |
| title_sort | markov chains |
| topic | Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Markov-Kette |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016244912&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
| work_keys_str_mv | AT norrisjamesr markovchains |