Degenerate diffusion operators arising in population biology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
2013
|
| Series: | Annals of mathematics studies
185 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 306 S. 25 cm |
| ISBN: | 9780691157122 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Degenerate diffusion operators arising in population biology
Autor: Epstein, Charles L
Jahr: 2013
Contents
Preface xi
1 Introduction 1
1.1 Generalized Kimura Diffusions..................... 3
1.2 Model Problems............................. 5
1.3 Perturbation Theory........................... 9
1.4 Main Results .............................. 10
1.5 Applications in Probability Theory................... 13
1.6 Alternate Approaches.......................... 14
1.7 Outline of Text............................. 16
1.8 Notational Conventions......................... 20
1 Wright-Fisher Geometry and the Maximum Principle 23
2 Wright-Fisher Geometry 25
2.1 Polyhedra and Manifolds with Corners................. 25
2.2 Normal Forms and Wright-Fisher Geometry.............. 29
3 Maximum Principles and Uniqueness Theorems 34
3.1 Model Problems............................. 34
3.2 Kimura Diffusion Operators on Manifolds with Corners........ 35
3.3 Maximum Principles for the Heat Equation .............. 45
II Analysis of Model Problems 49
4 The Model Solution Operators 51
4.1 The Model Problem in 1-dimension.................. 51
4.2 The Model Problem in Higher Dimensions............... 54
4.3 Holomorphic Extension......................... 59
4.4 First Steps Toward Perturbation Theory ................ 62
5 Degenerate Holder Spaces 64
5.1 Standard Holder Spaces......................... 65
5.2 WF-Hölder Spaces in 1-dimension................... 66
vii
viii CONTENTS
6 Holder Estimates for the 1-dimensional Model Problems 78
6.1 Kernel Estimates for Degenerate Model Problems........... 80
6.2 Holder Estimates for the 1-dimensional Model Problems....... 89
6.3 Properties of the Resolvent Operator.................. 103
7 Holder Estimates for Higher Dimensional Corner Models 107
7.1 The Cauchy Problem.......................... 109
7.2 The Inhomogeneous Case........................ 122
7.3 The Resolvent Operator......................... 135
8 Holder Estimates for Euclidean Models 137
8.1 Holder Estimates for Solutions in the Euclidean Case......... 137
8.2 1-dimensional Kernel Estimates .................... 139
9 Holder Estimates for General Models 143
9.1 The Cauchy Problem.......................... 145
9.2 The Inhomogeneous Problem...................... 149
9.3 Off-diagonal and Long-time Behavior................. 166
9.4 The Resolvent Operator......................... 169
III Analysis of Generalized Kimura Diffusions 179
10 Existence of Solutions 181
10.1 WF-Hölder Spaces on a Manifold with Corners............ 182
10.2 Overview of the Proof.......................... 187
10.3 The Induction Argument........................ 191
10.4 The Boundary Parametrix Construction ................ 194
10.5 Solution of the Homogeneous Problem................. 205
10.6 Proof of the Doubling Theorem..................... 208
10.7 The Resolvent Operator and Cn-Semi-group.............. 209
10.8 Higher Order Regularity ........................ 211
11 The Resolvent Operator 218
11.1 Construction of the Resolvent ..................... 220
11.2 Holomorphic Semi-groups....................... 229
11.3 Diffusions Where All Coefhcients Have the Same Leading Homogeneity 230
12 The Semi-group on %° (P) 235
12.1 The Domain of the Adjoint....................... 237
12.2 TheNull-spaceofI0.......................... 240
12.3 Long Time Asymptotics ........................ .243
12.4 Irregulär Solutions of the Inhomogeneous Equation.......... 247
CONTENTS ix
A Proofs of Estimates for the Degenerate 1-d Model 251
A.l Basic Kernel Estimates......................... 252
A.2 First Derivative Estimates........................ 272
A.3 Second Derivative Estimates...................... 278
A.4 Off-diagonal and Large-f Behavior................... 291
Bibliography 301
Index 305
|
| any_adam_object | 1 |
| author | Epstein, Charles L. 1957- Mazzeo, Rafe |
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| author_facet | Epstein, Charles L. 1957- Mazzeo, Rafe |
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| discipline | Mathematik |
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| id | DE-604.BV040958524 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:36:13Z |
| institution | BVB |
| isbn | 9780691157122 |
| language | English |
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| physical | XIII, 306 S. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | Princeton University Press |
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| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Epstein, Charles L. 1957- Verfasser (DE-588)133727807 aut Degenerate diffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo Princeton ; Oxford Princeton University Press 2013 XIII, 306 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 185 Mazzeo, Rafe Verfasser aut Annals of mathematics studies 185 (DE-604)BV000000991 185 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025936928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Epstein, Charles L. 1957- Mazzeo, Rafe Degenerate diffusion operators arising in population biology Annals of mathematics studies |
| title | Degenerate diffusion operators arising in population biology |
| title_auth | Degenerate diffusion operators arising in population biology |
| title_exact_search | Degenerate diffusion operators arising in population biology |
| title_full | Degenerate diffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_fullStr | Degenerate diffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_full_unstemmed | Degenerate diffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_short | Degenerate diffusion operators arising in population biology |
| title_sort | degenerate diffusion operators arising in population biology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025936928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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