Continuous time Markov chains: an applications-oriented approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1991
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 333 - 346 |
| Physical Description: | XII, 355 S. |
| ISBN: | 3540973699 0387973699 |
Staff View
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Record in the Search Index
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| adam_text | 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. Q Functions and the Kolmogorov Backward and Forward Equations 61
2. Existence and Uniqueness of Q 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
xii Contents
2. Sub invariant and Invariant Measures 166
3. Classification Based on the g Matrix 184
4. Determination of Invariant Measures from the Q 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. Geometric 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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| id | DE-604.BV004727843 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:16:47Z |
| institution | BVB |
| isbn | 3540973699 0387973699 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002907163 |
| oclc_num | 21907348 |
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| physical | XII, 355 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Anderson, William J. Verfasser aut Continuous time Markov chains an applications-oriented approach William J. Anderson New York u.a. Springer 1991 XII, 355 S. 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-Prozess (DE-588)4134948-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 s DE-604 Markov-Kette (DE-588)4037612-6 s Markov-Prozess (DE-588)4134948-9 s Zeitreihenanalyse (DE-588)4067486-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002907163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anderson, William J. Continuous time Markov chains an applications-oriented approach Markov, processus de ram Markov-processen gtt Processus de Markov Markov processes Markov-Prozess (DE-588)4134948-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4067486-1 (DE-588)4037612-6 (DE-588)4272650-5 |
| 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-Prozess (DE-588)4134948-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd |
| topic_facet | Markov, processus de Markov-processen Processus de Markov Markov processes Markov-Prozess Zeitreihenanalyse Markov-Kette Markov-Kette mit stetiger Zeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002907163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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