Birth and death processes and Markov chains:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1992
|
| Edition: | Rev. ed. of the orig. Chinese ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Chines. übers. |
| Physical Description: | IX, 361 S. |
| ISBN: | 3540108203 0387108203 7030022505 |
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MARC
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| 245 | 1 | 0 | |a Birth and death processes and Markov chains |c Wang Zikun ; Yang Xiangqun |
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| 264 | 1 | |a Berlin u.a. |b Springer |c 1992 | |
| 300 | |a IX, 361 S. | ||
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Record in the Search Index
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| adam_text | CONTENTS
Preface V
Chapter I General Concepts of Stochastic Processes 1
§1.1 Definition of Stochastic Processes 1
§1.2 Separability of Stochastic Processes 6
§1.3 Measurability of Stochastic Processes 11
§1.4 Conditional Probabilities
and Conditional Mathematical Expectations 15
§1.5 Markov Property 20
§1.6 Transition Probabilities 23
Chapter II Analytic Theory of Markov Chains 29
§2.1 General Properties of Measurable Transition Matrices 29
§22 Differentiability of Standard Transition Matrices 34
§2.3 Backward and Forward Differential Equations 49
§2.4 Standard Generalized Transition Matrices 61
§2.5 Resolvent Matrices 66
§2.6 The Minimal Q Resolvent Matrices 72
§2.7 Properties of the Minimal Q Resolvent Matrix 74
§2.8 Exit Families and Entrance Families 78
§2.9 General Forms of Q Resolvent Matrices 83
§2.10 Construction of Q Resolvent Matrices in Simple Cases 86
Chapter III Properties of Sample Functions 96
§3.1 Sets of Constancy and Intervals of Constancy 96
§3.2 Right Lower Semi Continuity; Canonical Chains 102
§33 Strong Markov Property 108
Chapter IV Some Topics in Markov Chains 112
§4.1 Zero One Laws 112
§42 Recurrence and Excessive Functions • 121
§4.3 Distributions of Stochastic Functionals of Integral Type 127
§4.4 Embedding Problem 138
Chapter V Basic Theory of Birth and Death Processes 146
§5.1 Probabilistic Meanings of Numerical Characteristics 146
§52 Random Functionals of Upward Integral Type 154
viii Contents
§53 First Entrance Time and Sojourn Time 167
§5.4 Random Functionate of Downward Integral Type 174
§5.5 Solutions of Several Types of Kolmogorov Equations
and Stationary Distributions 183
§5.6 Some Applications of Birth and Death Processes 194
Chapter VI Construction Theory of Birth and Death Processes 199
§6.1 Transformations of Doob Processes 199
§6.2 The Necessary and Sufficient Condition ;
that a Process Cannot Enter Continuously 207
§6.3 Transformation of General Q Processes
into Doob Processes 211
§6.4 Construction of Q Processes for S °° 215
§6.5 Characteristic Sequences and Classification of Birth
and Death Processes 225
§6.6 Fundamental Theorem 234
§6.7 Another Construction of Q Processes in Case S=°° 237
§6.8 Ergodic Property and Zero One Laws 240
Chapter VII Analytical Construction of Birth and Death Processes 244
§7.1 Natural Scale and Canonical Measure 244
§7.2 Second Order Difference Operators 245
§73 The Solution to the Equation Am—D//u+=0 249
§7.4 Construction of the Minimal Solution 251
§7.5 Some Lemmas 254
§7.6 Construction of the Q Resolvent Matrix of B Type 258
§7.7 Construction of the Q Resolvent Matrix of F Type 259
§7.8 Construction of Q Resolvent Matrices Neither of B Type
nor of F Type: In the Case of Linear Dependence 261
§7.9 Construction of Q Resolvent Matrices Neither of B Type
nor of F Type: In the Case of Linear Independence 265
§7.10 The Conditions for a f {X)€ 1 275
§7.11 Birth and Death Processes of Probability 277
§7.12 Relation Between Probabilistic and Analytic Constructions 286
§7.13 Properties of a Process on Its First Point of Flying Leap 290
§7.14 Invariant Measure 292
Chapter VIII Bilateral Birth and Death Processes 294
§8.1 Numerical Characteristics and Classification
of Boundary Points 294
§8.2 Solutions to the Equation Xu Duu+=0 295
§83 The Minimal Solution 299
§8.4 Representations for Exit and Entrance Families 301
§85 7, is Entrance or Natural and 7., is Regular or Exit 305
Contents ix
§8.6 Both /, and y2 are Regular or Exit 306
§8.7 Conditions for tt0(A)e / 309
§8.8 Properties of Boundaries 311
§8.9 Recurrence and Ergodicity 318
Appendix I Excessive Functions of Markov Chains
with Discrete Time 324
§0.1 Potential and Excessive Functions 324
§0.2 Limit Theorems on Excessive Functions 333
Appendix II A Systems and the S System Method 346
Annotations on the History of the Contents of Each Section 349
Bibliography 353
Index 360
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Rev. ed. of the orig. Chinese ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:25:24Z |
| institution | BVB |
| isbn | 3540108203 0387108203 7030022505 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005827937 |
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| physical | IX, 361 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| spelling | Wang, Zikun Verfasser aut Birth and death processes and Markov chains Wang Zikun ; Yang Xiangqun Rev. ed. of the orig. Chinese ed. Berlin u.a. Springer 1992 IX, 361 S. txt rdacontent n rdamedia nc rdacarrier Aus dem Chines. übers. Probabilities Birth and death processes (Stochastic processes) Markov processes Geburt-Tod-Prozess Mathematik (DE-588)4156185-5 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s DE-604 Geburt-Tod-Prozess Mathematik (DE-588)4156185-5 s Yang, Xiangqun Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005827937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Zikun Yang, Xiangqun Birth and death processes and Markov chains Probabilities Birth and death processes (Stochastic processes) Markov processes Geburt-Tod-Prozess Mathematik (DE-588)4156185-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4156185-5 (DE-588)4037612-6 |
| title | Birth and death processes and Markov chains |
| title_auth | Birth and death processes and Markov chains |
| title_exact_search | Birth and death processes and Markov chains |
| title_full | Birth and death processes and Markov chains Wang Zikun ; Yang Xiangqun |
| title_fullStr | Birth and death processes and Markov chains Wang Zikun ; Yang Xiangqun |
| title_full_unstemmed | Birth and death processes and Markov chains Wang Zikun ; Yang Xiangqun |
| title_short | Birth and death processes and Markov chains |
| title_sort | birth and death processes and markov chains |
| topic | Probabilities Birth and death processes (Stochastic processes) Markov processes Geburt-Tod-Prozess Mathematik (DE-588)4156185-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Probabilities Birth and death processes (Stochastic processes) Markov processes Geburt-Tod-Prozess Mathematik Markov-Kette |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005827937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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