Discrete-time Markov chains: two-time-scale methods and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2005
|
| Schriftenreihe: | Applications of mathematics
55 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIX, 347 S. graph. Darst. 24 cm |
| ISBN: | 038721948X 9781441919557 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV019732286 | ||
| 003 | DE-604 | ||
| 005 | 20150716 | ||
| 007 | t | ||
| 008 | 050311s2005 xxud||| |||| 00||| eng d | ||
| 010 | |a 2004049169 | ||
| 020 | |a 038721948X |c alk. paper |9 0-387-21948-X | ||
| 020 | |a 9781441919557 |9 978-1-4419-1955-7 | ||
| 035 | |a (OCoLC)55286549 | ||
| 035 | |a (DE-599)BVBBV019732286 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-29T |a DE-824 |a DE-91G |a DE-384 |a DE-355 |a DE-11 |a DE-188 |a DE-83 |a DE-706 | ||
| 050 | 0 | |a QA274.7 | |
| 082 | 0 | |a 519.2/33 |2 22 | |
| 082 | 0 | |a 519.233 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a MAT 607f |2 stub | ||
| 084 | |a 60J10 |2 msc | ||
| 100 | 1 | |a Yin, George |d 1954- |e Verfasser |0 (DE-588)115596798 |4 aut | |
| 245 | 1 | 0 | |a Discrete-time Markov chains |b two-time-scale methods and applications |c G. George Yin ; Qing Zhang |
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a XIX, 347 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 55 | |
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Discrete gebeurtenissen |2 gtt | |
| 650 | 4 | |a Markov, Processus de | |
| 650 | 7 | |a Markov-processen |2 gtt | |
| 650 | 4 | |a Markov processes | |
| 650 | 0 | 7 | |a Markov-Prozess |0 (DE-588)4134948-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Markov-Prozess |0 (DE-588)4134948-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Zhang, Qing |e Sonstige |4 oth | |
| 830 | 0 | |a Applications of mathematics |v 55 |w (DE-604)BV000895226 |9 55 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013059163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013059163 | ||
Datensatz im Suchindex
| _version_ | 1804133194736336896 |
|---|---|
| adam_text | Contents
Preface
xi
Conventions xv
Glossary of Symbols
xvii
Part I: Prologue and Preliminaries
1
1
Introduction, Overview, and Examples
3
1.1
Introduction
........................... 3
1.2
Brief Literature Review
.................... 6
1.3
Motivational Examples
..................... 8
1.4
Discrete-Time vs. Continuous-Time Models
......... 17
1-5
Organization
.......................... 19
2
Mathematical Preliminaries
25
2.1
Introdviction
........................... 25
2.2
Discrete-Time Markov Chains
................. 25
2.3
Discrete-Time Martingales
................... 28
2.4
Continuous-Tune
Martingale»
and Markov Chains
..... 30
2.5
Gaussian, Diffusion, and Switching Diffusion Processes
. . . 36
2.6
Notes
.............................. 38
Part II: Asymptotic Properties
41
Asymptotic Expansions
43
3.1
Introduction
........................... 43
3.1.1
Why Do We Need Asymptotic Expansions?
..... 44
3.1.2
Outline of the Chapter
................. 46
3.2
Formulation and Conditions
.................. 47
3.2.1
Decomposition and Subspaces
............. 48
3.2.2
Asymptotic Expansions
................ 48
3.3
Asymptotic Expansions: Irreducible Case
.......... 48
3.4
Asymptotic Expansions: General Case
............ 52
3.4.1
Constructing -fio(ek) and
-фо(к)
............ 54
3.4.2
Constructing
ψη(ί)
and
фп{к)
for
η
> 1....... 57
3.5
Error Bounds
..................... ..... 59
3.5.1
Estimates on CEe%
(к)
................. 59
3.5.2
An Estimate of
4
(¿fe)
................. 60
3.5.3
Expansions of ¿fc-step Transition Matrices
...... 01
3.6
Examples
............................ 63
3.7
Proofs of Results
........................ 65
3.8
Notes
.............................. 67
Occupation Measures
69
4.1
Introduction
........................... 69
4.2
Irreducible Chains
....................... 71
4.2.1
A Motivational Example
................ 71
4.2.2
Discussion
........................ 73
4.3
Recurrent States
........................ 77
4.3.1
Formulation and Preliminary
............. 77
4.3.2
Aggregation
....................... 78
4.3.3
Asymptotic Distribution
................ 79
4.4
Inclusion of Transient States
.................. 82
4.5
Proofs of Results
........................ 84
4.6
Notes
.............................. 102
Exponential Bounds
103
5.1
Introduction
........................... 103
5.2
Formulation
........................... 104
5.3
Main Results
.......................... 104
5.3.1
Irreducible Chains
................... 104
5.3.2
Recurrent Chains
.................... 106
5.3.3
Markov Chains with Transient States
........ 107
5.4
Applications
........................... 108
5.5
Proofs of Results
........................ 109
5.6
Notes
.............................. 118
Interim Summary and Extensions
119
6.1
Introduction
.......................... 119
6.2
The Model
........................... 120
6.
3
Recurrent Chains
........................ 121
6.4
Inclusion of Transient States
.................. 124
6.5
Nonstationary Markov Chains
................. 127
6.6
Notes
.............................. 129
Part III: Applications
131
7
Stability of Dynamic Systems
133
7.1
Introduction
........................... 133
7.2
Formulation
........................... 134
7.2.1
Problem Setup
..................... 135
7.2.2
Demonstrative Examples
............... 136
7.3
Preliminary Results
...................... 136
7.4
Stability
............................. 139
7.5
Recurrence and Path Excursion
................ 142
7.6
Proofs of Results
........................ 143
7.7
Remarks
............................. 156
7.7.1
Extensions
....................... 156
7.7.2
Further Investigation
.................. 157
7.8
Notes
.............................. 157
8
Filtering
159
8.1
Introduction
........................... 159
8.2
Main Results
.......................... 161
8.2.1
Formulation
....................... 161
8.2.2
Near-Optimal Filtering
................ 163
8.3
Proofs of Results
......................... 168
8.4
Discrete-Time Approximation of Wonham Filter
...... 184
8.5
Notes
.............................. 191
9
Markov Decision Processes
195
9.1
Introduction
........................... 195
9.2
Discounted Cost
........................ 196
9.3
Long-Run Average Cost
.................... 204
9.4
An Example
..... ...................... 207
9.5
Proofs of Results
........................ 210
9.6
Notes
.............................. 222
10
LQ Controls
225
10.1
Introduction
........................... 225
10.2
Problem Formulation
...................... 226
10.3
Main Results
.......................... 231
10.4
Numerical Example
....................... 234
10.4.1
A Scalar LQ System
.................. 234
10.4.2
A Vector-Valued LQ System
............. 236
10.4.3
Remarks
......................... 237
10.5
Proofs of Results
........................ 238
10.6
Notes
.............................. 249
11
Mean-Variance Controls
251
11.1
Introduction
........................... 251
11.2
Formulation
........................... 252
11.2.1
Limit Results
...................... 255
11.2.2
Weak Convergence
................... 256
11.3
Near-Efficient Portfolio
..................... 259
11.4
Inclusion of Transient States
.................. 260
11.5
Continuous-Time Problems
.................. 260
11.6
Proofs of Results
........................ 262
11.7
Notes
.............................. 269
12
Production Planning
271
12.1
Introduction
........................... 271
12.2
Main Results
.......................... 272
12.3
Examples
............................ 276
12.4
Proofs of Results
........................ 279
12.5
Notes
.............................. 284
13
Stochastic Approximation
285
13.1
Introduction
........................... 285
13.2
Problem Formulation
...................... 287
13.3
Algorithm
............................ 289
13.4
Asymptotic Properties
..................... 289
13.4.1
Mean Squares Error
.................. 289
13.4.2
Limit Switching ODEs
................. 290
13.4.3
Switching Diffusion Limit
............... 292
13.4.4
Probability Error Bounds
............... 295
13.5
Proofs of Results
........................ 297
13.6
Notes
.............................. 312
14
Appendix
315
14.1
Introduction
...........:............... 315
14.2
Sample Paths of Markov Chains
............... 315
14.3
Weak Convergence
....................... 316
14.4
Optimal Controls and H.TB Equations
............ 324
14.5
Miscellany
............................ 328
14.6
Notes
.............................. 332
References
333
Index
345
|
| any_adam_object | 1 |
| author | Yin, George 1954- |
| author_GND | (DE-588)115596798 |
| author_facet | Yin, George 1954- |
| author_role | aut |
| author_sort | Yin, George 1954- |
| author_variant | g y gy |
| building | Verbundindex |
| bvnumber | BV019732286 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.7 |
| callnumber-search | QA274.7 |
| callnumber-sort | QA 3274.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 607f |
| ctrlnum | (OCoLC)55286549 (DE-599)BVBBV019732286 |
| dewey-full | 519.2/33 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 519.233 |
| dewey-search | 519.2/33 519.233 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01979nam a2200517zcb4500</leader><controlfield tag="001">BV019732286</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150716 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">050311s2005 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2004049169</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">038721948X</subfield><subfield code="c">alk. paper</subfield><subfield code="9">0-387-21948-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441919557</subfield><subfield code="9">978-1-4419-1955-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)55286549</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019732286</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="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/33</subfield><subfield code="2">22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.233</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="084" ind1=" " ind2=" "><subfield code="a">60J10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yin, George</subfield><subfield code="d">1954-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115596798</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Discrete-time Markov chains</subfield><subfield code="b">two-time-scale methods and applications</subfield><subfield code="c">G. George Yin ; Qing Zhang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 347 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="c">24 cm</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">Applications of mathematics</subfield><subfield code="v">55</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Discrete gebeurtenissen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov, Processus de</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Markov-processen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov processes</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-Prozess</subfield><subfield code="0">(DE-588)4134948-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Qing</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applications of mathematics</subfield><subfield code="v">55</subfield><subfield code="w">(DE-604)BV000895226</subfield><subfield code="9">55</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=013059163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-013059163</subfield></datafield></record></collection> |
| id | DE-604.BV019732286 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:04:51Z |
| institution | BVB |
| isbn | 038721948X 9781441919557 |
| language | English |
| lccn | 2004049169 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013059163 |
| oclc_num | 55286549 |
| open_access_boolean | |
| owner | DE-29T DE-824 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-11 DE-188 DE-83 DE-706 |
| owner_facet | DE-29T DE-824 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-11 DE-188 DE-83 DE-706 |
| physical | XIX, 347 S. graph. Darst. 24 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Yin, George 1954- Verfasser (DE-588)115596798 aut Discrete-time Markov chains two-time-scale methods and applications G. George Yin ; Qing Zhang New York, NY Springer 2005 XIX, 347 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 55 Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke Discrete gebeurtenissen gtt Markov, Processus de Markov-processen gtt Markov processes Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s DE-604 Zhang, Qing Sonstige oth Applications of mathematics 55 (DE-604)BV000895226 55 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013059163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yin, George 1954- Discrete-time Markov chains two-time-scale methods and applications Applications of mathematics Discrete gebeurtenissen gtt Markov, Processus de Markov-processen gtt Markov processes Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4134948-9 |
| title | Discrete-time Markov chains two-time-scale methods and applications |
| title_auth | Discrete-time Markov chains two-time-scale methods and applications |
| title_exact_search | Discrete-time Markov chains two-time-scale methods and applications |
| title_full | Discrete-time Markov chains two-time-scale methods and applications G. George Yin ; Qing Zhang |
| title_fullStr | Discrete-time Markov chains two-time-scale methods and applications G. George Yin ; Qing Zhang |
| title_full_unstemmed | Discrete-time Markov chains two-time-scale methods and applications G. George Yin ; Qing Zhang |
| title_short | Discrete-time Markov chains |
| title_sort | discrete time markov chains two time scale methods and applications |
| title_sub | two-time-scale methods and applications |
| topic | Discrete gebeurtenissen gtt Markov, Processus de Markov-processen gtt Markov processes Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Discrete gebeurtenissen Markov, Processus de Markov-processen Markov processes Markov-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013059163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT yingeorge discretetimemarkovchainstwotimescalemethodsandapplications AT zhangqing discretetimemarkovchainstwotimescalemethodsandapplications |