Branching processes with biological applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Wiley
[1975]
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| Series: | Wiley series in probability and mathematical statistics, applied
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 268 Seiten Illustrationen |
| ISBN: | 0471436526 |
Staff View
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Branching processes | |
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Record in the Search Index
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Contents
A List of Symbols and Notation Conventions xi
1 Introduction 1
1.1 Historical sketch 1
1.2 Generalities about populations 5
1.3 A survey of results 9
2 The Galton-Watson Process 19
2.1 Introduction 19
2.2 Moments and the generating function 20
2.3 The extinction probability 22
2.4 Critical processes 24
2.5 A simple but basic lemma 26
2.6 Subcritical processes 28
2.7 Supercritical processes 30
2.8 Attaining high levels 35
2.9 Rate of convergence results for supercritical processes 36
2.10 Prediction in large supercritical processes and another rate
of convergence result 37
2.11 The total progeny of a branching process 39
2.12 The relation between a process and its total progeny 42
2.13 Maximum likelihood estimation of the reproduction mean
and a Bayes example 45
2.14 Estimation of the extinction probability 50
3 Neighbours of the Galton-Watson Process 54
3.1 Branching processes with immigration 54
3.2 Increasing numbers of ancestors 60
3.3 Approximation by critical processes 63
3.4 A diffusion approximation 67
3.5 Galton-Watson processes in varying environments 70
3.6 Further results for varying environments 77
3.7 Random environments 81
viii
CONTENTS ix
4 Results for Multi-type Processes 87
4.1 Fundamentals 87
4.2 Analogues of classical results 92
5 Interlude about Martingales, Renewal Theory, and Point
Processes 97
5.1 Martingales 97
5.2 The renewal equation 104
5.3 Refined renewal theorems 114
5.4 Point processes 120
6 The General Process 123
6.1 Introduction 123
6.2 The finiteness of the process 126
6.3 Moments and the generating functions 129
6.4 More about the second moments 135
6.5 The extinction probability 139
6.6 Critical processes 143
6.7 The subcritical case 156
6.8 Supercritical processes 164
6.9 Populations counted with random characteristics 167
6.10 Almost sure convergence in the supercritical case 169
6.11 The stable age distribution and processes with an ancestor
differing from its progeny 176
6.12 The total progeny 182
6.13 Integrals of branching processes and their generalizations 183
6.14 Maximum likelihood estimation of the reproduction mean 186
7 Neighbours of the General Process 190
7.1 Immigration 190
7.2 Increasing numbers of ancestors 199
7.3 Convergence towards criticality 200
7.4 Diffusion approximations 202
8 Branching Processes and Demography 207
8.1 Classical continuous time demography and age dependent
birth and death processes 207
8.2 Lotka's equation 209
8.3 The growth of populations 211
8.4 The age at childbearing 214
8.5 The length of generations 215
t
X CONTENTS
9 Branching Models in Cell Kinetics 224
9.1 Cell proliferation and binary splitting 224
9.2 Estimation of cell death 228
9.3 The cycle time distribution 230
9.4 The fraction labelled mitoses 232
9.5 FLM functions in binary splitting 236
9.6 Continuous labelling 241
9.7 Arrest methods 245
9.8 Synchrony 248
9.9 The composition of two-type populations: endomitosis and
the Go resting phase 250
Appendix 259
Index 265 |
| any_adam_object | 1 |
| author | Jagers, Peter 1941- |
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| dewey-full | 574.5/24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 574 - [Unassigned] |
| dewey-raw | 574.5/24 |
| dewey-search | 574.5/24 |
| dewey-sort | 3574.5 224 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV003072973 |
| illustrated | Illustrated |
| indexdate | 2024-08-30T00:16:52Z |
| institution | BVB |
| isbn | 0471436526 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001926546 |
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| physical | xiii, 268 Seiten Illustrationen |
| publishDate | 1975 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics, applied |
| spelling | Jagers, Peter 1941- (DE-588)131866524 aut Branching processes with biological applications P. Jagers London [u.a.] Wiley [1975] © 1975 xiii, 268 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics, applied Biologie des populations - Modèles mathématiques Processus ramifiés Mathematisches Modell Branching processes Population biology Mathematical models Verzweigungsprozess (DE-588)4188184-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Verzweigungsprozess (DE-588)4188184-9 s Biologie (DE-588)4006851-1 s DE-604 Populationsbiologie (DE-588)4046800-8 s Mathematisches Modell (DE-588)4114528-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001926546&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jagers, Peter 1941- Branching processes with biological applications Biologie des populations - Modèles mathématiques Processus ramifiés Mathematisches Modell Branching processes Population biology Mathematical models Verzweigungsprozess (DE-588)4188184-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Biologie (DE-588)4006851-1 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| subject_GND | (DE-588)4188184-9 (DE-588)4114528-8 (DE-588)4006851-1 (DE-588)4046800-8 |
| title | Branching processes with biological applications |
| title_auth | Branching processes with biological applications |
| title_exact_search | Branching processes with biological applications |
| title_full | Branching processes with biological applications P. Jagers |
| title_fullStr | Branching processes with biological applications P. Jagers |
| title_full_unstemmed | Branching processes with biological applications P. Jagers |
| title_short | Branching processes with biological applications |
| title_sort | branching processes with biological applications |
| topic | Biologie des populations - Modèles mathématiques Processus ramifiés Mathematisches Modell Branching processes Population biology Mathematical models Verzweigungsprozess (DE-588)4188184-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Biologie (DE-588)4006851-1 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| topic_facet | Biologie des populations - Modèles mathématiques Processus ramifiés Mathematisches Modell Branching processes Population biology Mathematical models Verzweigungsprozess Biologie Populationsbiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001926546&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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