Finite Markov processes and their applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
[1980]
Bucureşti Ed. Tehnică |
| Schriftenreihe: | Wiley series in probability and mathematical statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510713&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus d. Rumän. übers. - Literaturverz. S. [275] - 289 |
| Umfang: | 295 Seiten Illustrationen |
| ISBN: | 0471276774 |
Internformat
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| 100 | 1 | |a Iosifescu, Marius |d 1936-2020 |0 (DE-588)107476444 |4 aut | |
| 240 | 1 | 0 | |a Lanţuri Markov finite şi aplicaţii |
| 245 | 1 | 0 | |a Finite Markov processes and their applications |c Marius Iosifescu |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c [1980] | |
| 264 | 1 | |a Bucureşti |b Ed. Tehnică | |
| 264 | 4 | |c © 1980 | |
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| 490 | 0 | |a Wiley series in probability and mathematical statistics | |
| 500 | |a Aus d. Rumän. übers. - Literaturverz. S. [275] - 289 | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 607f 2001 A 19086 0740 M.3.2888 |
|---|---|
| DE-BY-TUM_katkey | 388814 |
| DE-BY-TUM_location | 01 LSB |
| DE-BY-TUM_media_number | 040020417309 TEMP3152817 |
| _version_ | 1821940902557384704 |
| adam_text | Contents
Introduction 13
CHAPTER 1 ELEMENTS OF PROBABILITY THEORY AND
LINEAR ALGEBRA 17
1.1 Random events 17
1.2 Probability 20
1.3 Dependence and independence 24
1.4 Random variables. Mean values 26
1.5 Random processes 36
1.6. Matrices 38
1.7 Operations with matrices 41
1.8 r dimensional space 46
1.9 Eigenvalues and eigenvectors Al
1.10 Nonnegative matrices. The Perron Frobenius theorems 51
1.11 Stochastic matrices. Ergodicity coefficients 54
CHAPTER 2 FUNDAMENTAL CONCEPTS IN HOMOGENEOUS
MARKOV CHAIN THEORY 60
2.1 The Markov property 60
2.2 Examples of homogeneous Markov chains 66
2.3 Stopping times and the strong Markov property 11
1A Classes of states 80
2.5 Recurrence and transience 86
2.6 Classification of homogeneous Markov chains 94
Exercises 96
CHAPTER 3 ABSORBING MARKOV CHAINS 99
3.1 The fundamental matrix 99
3.2 Applications of the fundamental matrix 101
3.3 Extensions and complements 113
3.4 Conditional transient behaviour 116
Exercises 119
CHAPTER 4 ERGODIC MARKOV CHAINS 122
4.1 Regular Markov chains 122
4.2 The stationary distribution 128
4.3 The fundamental matrix 132
10 Contents
4.4 Cyclic Markov chains 141
4.5 Reversed Markov chains 143
4.6 The Ehrenfest model 145
Exercises 149
CHAPTER 5 GENERAL PROPERTIES OF MARKOV CHAINS 153
5.1 Asymptotic behaviour of transition probabilities 153
5.2 The tail a algebra 158
5.3 Limit theorems for partial sums 162
5.4 Grouped Markov chains 166
5.5 Expanded Markov chains 173
5.6 Extending the concept of a homogeneous finite Markov chain 175
Exercises 111
CHAPTER 6 APPLICATIONS OF MARKOV CHAINS IN
PSYCHOLOGY AND GENETICS 180
6.1 Mathematical learning theory 180
6.2 The pattern model 181
6.3 The Markov chain associated with the pattern model 186
6.4 The Mendelian theory of inheritance 192
6.5 Sib mating 195
6.6 Genetic drift. The Wright model 199
Exercises 209
CHAPTER 7 NONHOMOGENEOUS MARKOV CHAINS 213
7.1 Generalities 213
7.2 Weak ergodicity 217
7.3 Uniform weak ergodicity 221
7.4 Strong ergodicity 223
7.5 Uniform strong ergodicity 226
7.6 Asymptotic behaviour of nonhotnogeneous Markov chains 229
Exercises 232
CHAPTER 8 MARKOV PROCESSES 234
8.1 Measure theoretical definition of a Markov process 234
8.2 The intensity matrix 236
8.3 Constructive definition of a Markov process TAT.
8.4 Discrete skeletons and classification of states 246
8.5 Absorbing Markov processes 249
Contents I
8.6 Regular Markov processes 253
8.7 Birth and death processes 257
8.8 Extending the concept of a homogeneous finite Markov process 260
8.9 Nonhotnogeneous Markov processes 262
Exercises 267
Historical Notes 273
Bibliography 275
List of Symbols 291
Subject Index 293
|
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| author | Iosifescu, Marius 1936-2020 |
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| author_role | aut |
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| author_variant | m i mi |
| building | Verbundindex |
| bvnumber | BV002298509 |
| classification_rvk | QH 237 SK 820 |
| ctrlnum | (OCoLC)472104805 (DE-599)BVBBV002298509 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV002298509 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:49:07Z |
| institution | BVB |
| isbn | 0471276774 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001510713 |
| oclc_num | 472104805 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-945 DE-29T DE-19 DE-BY-UBM DE-20 DE-706 DE-83 DE-11 DE-188 |
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| physical | 295 Seiten Illustrationen |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Wiley Ed. Tehnică |
| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spellingShingle | Iosifescu, Marius 1936-2020 Finite Markov processes and their applications Endliche Markov-Kette (DE-588)4152154-7 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4152154-7 (DE-588)4134948-9 |
| title | Finite Markov processes and their applications |
| title_alt | Lanţuri Markov finite şi aplicaţii |
| title_auth | Finite Markov processes and their applications |
| title_exact_search | Finite Markov processes and their applications |
| title_full | Finite Markov processes and their applications Marius Iosifescu |
| title_fullStr | Finite Markov processes and their applications Marius Iosifescu |
| title_full_unstemmed | Finite Markov processes and their applications Marius Iosifescu |
| title_short | Finite Markov processes and their applications |
| title_sort | finite markov processes and their applications |
| topic | Endliche Markov-Kette (DE-588)4152154-7 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Endliche Markov-Kette Markov-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510713&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT iosifescumarius lanturimarkovfinitesiaplicatii AT iosifescumarius finitemarkovprocessesandtheirapplications |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 607f 2001 A 19086
Lageplan |
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| Exemplar 1 | Ausleihbar Am Standort |
Handapparate (nicht verfügbar)
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0740 M.3.2888
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