Continuous-time Markov chains: an applications-oriented approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
1991
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 333 - 346 |
| Beschreibung: | xii, 355 Seiten |
| ISBN: | 0387973699 3540973699 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804120667759575040 |
|---|---|
| adam_text | IMAGE 1
WILLIAM J. ANDERSON
CONTINUOUS-TIME
MARKOV CHAINS AN APPLICATIONS-ORIENTED APPROACH
SPRINGER-VERLAG NEW YORK BERLIN HEIDELBERG LONDON PARIS TOKYO HONGKONG
BARCELONA BUDAPEST
IMAGE 2
CONTENTS
PREFACE VII
CHAPTER 1 TRANSITION FUNCTIONS AND RESOLVENTS 1. MARKOV CHAINS AND
TRANSITION FUNCTIONS: DEFINITIONS AND BASIC PROPERTIES 1 2.
DIFFERENTIABILITY PROPERTIES OF TRANSITION FUNCTIONS AND SIGNIFICANCE OF
THE
Q-MATRIX 8
3. RESOLVENT FUNCTIONS AND THEIR PROPERTIES 21
4. THE FUNCTIONAL-ANALYTIC SETTING FOR TRANSITION FUNCTIONS AND
RESOLVENTS .. 33 5. FELLER TRANSITION FUNCTIONS 42
6. KENDALL S REPRESENTATION OF REVERSIBLE TRANSITION FUNCTIONS 48
7. APPENDIX 54
CHAPTER 2 EXISTENCE AND UNIQUENESS OF Q-FUNCTIONS 1. SS-FUNCTIONS AND THE
KOLMOGOROV BACK WARD AND FORWARD EQUATIONS 61
2. EXISTENCE AND UNIQUENESS OF SS-FUNCTIONS 67
CHAPTER 3 EXAMPLES OF CONTINUOUS-TIME MARKOV CHAINS 1. FINITE MARKOV
CHAINS 92
2. BIRTH AND DEATH PROCESSES 96
3. CONTINUOUS TIME PARAMETER MARKOV BRANCHING PROCESSES 113
CHAPTER 4 MORE ON THE UNIQUENESS PROBLEM 1. LAPLACE TRANSFORM TOOLS 120
2. NON-UNIQUENESS-CONSTRUCTION OF Q-FUNCTIONS OTHER THAN THE MINIMAL ONE
138
3. UNIQUENESS-THE NON-CONSERVATIVE CASE 148
CHAPTER 5 CLASSIFICATION OF STATES AND INVARIANT MEASURES 1.
CLASSIFICATION OF STATES 155
IMAGE 3
XII CONTENTS
2. SUB-INVARIANT AND INVARIANT MEASURES 166
3. CLASSIFICATION BASED ON THE G-MATRIX 184
4. DETERMINATION OF INVARIANT MEASURES FROM THE SS-MATRIX 191
CHAPTER 6 STRONG AND EXPONENTIAL ERGODICITY 1. THE ERGODIC COEFFICIENT
AND HITTING TIMES 204
2. ORDINARY ERGODICITY 212
3. STRONG ERGODICITY 214
4. GEOMETRIE ERGODICITY FOR DISCRETE TIME CHAINS 217
5. THE CROFT-KINGMAN LEMMAS 224
6. EXPONENTIAL ERGODICITY FOR CONTINUOUS-TIME CHAINS 226
CHAPTER 7 REVERSIBILITY, MONOTONICITY, AND OTHER PROPERTIES 1. SYMMETRY
AND REVERSIBILITY 233
2. EXPONENTIAL FAMILIES OF TRANSITION FUNCTIONS 243
3. STOCHASTIC MONOTONICITY AND COMPARABILITY 246
4. DUAL PROCESSES 251
5. COUPLING 254
CHAPTER 8 BIRTH AND DEATH PROCESSES 1. THE POTENTIAL COEFFICIENTS AND
FELLER S BOUNDARY CONDITIONS 261
2. KARLIN AND MCGREGOR S REPRESENTATION THEOREM AND DUALITY 264
3. THE STIELTJES MOMENT PROBLEM 273
4. THE KARLIN-MCGREGOR METHOD OF SOLUTION 280
5. TOTAL POSITIVITY OF THE BIRTH AND DEATH TRANSITION FUNCTION 288
CHAPTER 9 POPULATION PROCESSES 1. UPWARDLY SKIP-FREE PROCESSES 292
2. EXTINCTION TIMES AND PROBABILITY OF EXTINCTION FOR UPWARDLY SKIP-FREE
PROCESSES 298
3. MULTIDIMENSIONAL POPULATION PROCESSES 307
4. TWO-DIMENSIONAL COMPETITION PROCESSES 317
5. BIRTH, DEATH, AND MIGRATION PROCESSES 330
BIBLIOGRAPHY 333
SYMBOL INDEX 347
AUTHOR INDEX 349
SUBJECT INDEX 351
|
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| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273 |
| callnumber-search | QA273 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV006418696 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:45:44Z |
| institution | BVB |
| isbn | 0387973699 3540973699 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004065755 |
| oclc_num | 21907348 |
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| physical | xii, 355 Seiten |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Anderson, William J. 1943- (DE-588)14205898X aut Continuous-time Markov chains an applications-oriented approach William J. Anderson 1. print. New York Springer 1991 xii, 355 Seiten txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 333 - 346 Markov, processus de ram Markov-processen gtt Processus de Markov Markov processes Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Markov-Kette mit stetiger Zeit (DE-588)4272650-5 s 1\p DE-604 Markov-Kette (DE-588)4037612-6 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-3038-0 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004065755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 | Anderson, William J. 1943- Continuous-time Markov chains an applications-oriented approach Markov, processus de ram Markov-processen gtt Processus de Markov Markov processes Markov-Kette (DE-588)4037612-6 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4037612-6 (DE-588)4272650-5 (DE-588)4134948-9 (DE-588)4067486-1 |
| title | Continuous-time Markov chains an applications-oriented approach |
| title_auth | Continuous-time Markov chains an applications-oriented approach |
| title_exact_search | Continuous-time Markov chains an applications-oriented approach |
| title_full | Continuous-time Markov chains an applications-oriented approach William J. Anderson |
| title_fullStr | Continuous-time Markov chains an applications-oriented approach William J. Anderson |
| title_full_unstemmed | Continuous-time Markov chains an applications-oriented approach William J. Anderson |
| title_short | Continuous-time Markov chains |
| title_sort | continuous time markov chains an applications oriented approach |
| title_sub | an applications-oriented approach |
| topic | Markov, processus de ram Markov-processen gtt Processus de Markov Markov processes Markov-Kette (DE-588)4037612-6 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Markov, processus de Markov-processen Processus de Markov Markov processes Markov-Kette Markov-Kette mit stetiger Zeit Markov-Prozess Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004065755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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