An introduction to superprocesses:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2000]
|
| Series: | University lecture series
Volume 20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 187 Seiten Illustrationen, Diagramme |
| ISBN: | 0821827065 9780821827062 |
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MARC
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| 100 | 1 | |a Etheridge, Alison |d 1964- |e Verfasser |0 (DE-588)114917531 |4 aut | |
| 245 | 1 | 0 | |a An introduction to superprocesses |c Alison M. Etheridge |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2000] | |
| 264 | 4 | |c © 2000 | |
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Record in the Search Index
| _version_ | 1804128050007244800 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 1. Superprocesses as Diffusion Approximatioas 1
Summary 1
The Dawson Watanabe superprocess 1
1.1. Branching Brownian motion 1
1.2. A martingale characterisation 4
1.3. The Feller diffusion 7
1.4. Rescaling and tightness 8
1.5. The Dawson Watanabe martingale problem 13
1.6. The method of duality 16
1.7. A more general class of superprocesses 17
1.8. Infinite initial measures 22
1.9. Historical superprocesses 24
The Fleming Viot superprocess 25
1.10. The stepwise mutation model 25
1.11. The Fleming Viot martingale problem 27
1.12. A dual process for Fleming Viot 29
Chapter 2. Qualitative Behaviour I 33
Summary 33
The Dawson Watanabe superprocess via its dual 33
2.1. A series solution to the evolution equation 33
2.2. Moments of the Dawson Watanabe superprocess 37
2.3. The density in one dimension 40
2.4. The spde viewpoint 42
2.5. Occupation times 44
2.6. Continuity and discontinuity 47
2.7. The extinction/persistence dichotomy 49
The Fleming Viot superprocess: first properties 55
2.8. Moments 55
2.9. The density in one dimension 56
Chapter 3. The Le Gall Representation 57
Summary 57
3.1. The branching process in random walk 57
3.2. The Feller rescaling (again) 59
3.3. The Evans Immortal Particle 60
3.4. Other skeletons 63
3.5. Le Jan s construction 64
vii
viii CONTENTS
3.6. The Brownian Snake 67
3.7. The infinite variance snake 69
3.8. Superprocesses and subordination 72
Chapter 4. The Relationship Between Our Two Classes of Superprocess 77
Summary 77
4.1. Approximating particle systems revisited 77
4.2. Generators revisited 78
4.3. The generator in polar coordinates 80
4.4. Consequences of the polar form of the generator 81
Chapter 5. A Countable Representation 85
Summary 85
5.1. A second look at the moment equations for Fleming Viot 85
5.2. The lookdown process 86
5.3. The modified Donnelly Kurtz construction 90
5.4. Incorporating selection 95
5.5. Some old results revisited 102
Chapter 6. Qualitative Behaviour II 105
Summary 105
6.1. Cluster representations 106
6.2. The historical modulus of continuity 108
6.3. The Hausdorff measure of the support 111
6.4. Palm distributions for the Dawson Watanabe superprocess 116
6.5. Charging and hitting sets 118
6.6. Intersection and collision local times 121
Chapter 7. Introducing Interactions 125
Summary 125
7.1. The basic superprocesses as building blocks 125
Perkins stochastic calculus 127
7.2. A discrete approximation 127
7.3. A countable representation 129
7.4. Dawson s Girsanov transform 133
7.5. Nonlinear branching 138
7.6. The Fleming Viot process with selection 139
7.7. A bivariate Girsanov transform 140
Chapter 8. Superprocesses and Partial Differential Equations 143
Summary 143
8.1. Exit measure 144
8.2. Solving a nonlinear Dirichlet problem 146
8.3. Polar sets and capacity 149
8.4. Le Gall s representation of solutions and related results 152
8.5. Super regularity of boundary points 154
Chapter 9. Some More Interacting Models 157
Summary 157
9.1. Multi level superprocesses 157
9.2. Competing species superprocesses 160
CONTENTS IX
9.3. Rescaling the contact process 162
9.4. Catalytic Superprocesses 165
9.5. Mutually catalytic superprocesses 168
Appendix 173
A.I. Kurtz s tightness criterion 173
A.2. Ordered binary rooted trees 173
A.3. White noise 174
A.4. Gronwall s inequality 175
Bibliography 177
Index of Notation 183
Index 185
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013283237 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:04Z |
| institution | BVB |
| isbn | 0821827065 9780821827062 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009055507 |
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| physical | xii, 187 Seiten Illustrationen, Diagramme |
| publishDate | 2000 |
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| publisher | American Mathematical Society |
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| series | University lecture series |
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| spelling | Etheridge, Alison 1964- Verfasser (DE-588)114917531 aut An introduction to superprocesses Alison M. Etheridge Providence, Rhode Island American Mathematical Society [2000] © 2000 xii, 187 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 20 Stochastischer Prozess - Zufälliges Maß - Zustandsraum Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zufälliges Maß (DE-588)4068049-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zufälliges Maß (DE-588)4068049-6 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2167-0 University lecture series Volume 20 (DE-604)BV004153846 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009055507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Etheridge, Alison 1964- An introduction to superprocesses University lecture series Stochastischer Prozess - Zufälliges Maß - Zustandsraum Stochastischer Prozess (DE-588)4057630-9 gnd Zufälliges Maß (DE-588)4068049-6 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4068049-6 (DE-588)4113937-9 |
| title | An introduction to superprocesses |
| title_auth | An introduction to superprocesses |
| title_exact_search | An introduction to superprocesses |
| title_full | An introduction to superprocesses Alison M. Etheridge |
| title_fullStr | An introduction to superprocesses Alison M. Etheridge |
| title_full_unstemmed | An introduction to superprocesses Alison M. Etheridge |
| title_short | An introduction to superprocesses |
| title_sort | an introduction to superprocesses |
| topic | Stochastischer Prozess - Zufälliges Maß - Zustandsraum Stochastischer Prozess (DE-588)4057630-9 gnd Zufälliges Maß (DE-588)4068049-6 gnd |
| topic_facet | Stochastischer Prozess - Zufälliges Maß - Zustandsraum Stochastischer Prozess Zufälliges Maß Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009055507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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