Diffusions, superdiffusions and partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2002
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| Series: | American Mathematical Society Colloquium publications
volume 50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 236 Seiten Illustrationen, Diagramme |
| ISBN: | 0821831747 |
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MARC
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| adam_text | AMERICAN MATHEMATICAL SOCIETY COLLOQUIUM PUBLICATIONS VOLUME 50
DIFFUSIONS, SUPERDIFFUSIONS AND PARTIAL DIFFERENTIAL EQUATIONS E. B.
DYNKIN FVDED AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND
CONTENTS PREFACE CHAPTER 1. INTRODUCTION 1 1. BROWNIAN AND
SUPER-BROWNIAN MOTIONS AND DIFFERENTIAL EQUATIONS 1 2. EXCEPTIONAL SETS
IN ANALYSIS AND PROBABILITY 5 3. POSITIVE SOLUTIONS AND THEIR BOUNDARY
TRACES 7 PART 1. PARABOLIC EQUATIONS AND BRANCHING EXIT MARKOV SYSTEMS
11 CHAPTER 2. LINEAR PARABOLIC EQUATIONS AND DIFFUSIONS 13 1.
FUNDAMENTAL SOLUTION OF A PARABOLIC EQUATION 13 2. DIFFUSIONS 15 3.
POISSON OPERATORS AND PARABOLIC FUNCTIONS 18 4. REGULAR PART OF THE
BOUNDARY 22 5. GREEN S OPERATORS AND EQUATION II + LU * * P 27 6. NOTES
30 CHAPTER 3. BRANCHING EXIT MARKOV SYSTEMS 33 1. INTRODUCTION 33 2.
TRANSITION OPERATORS AND V-FAMILIES 36 3. FROM A V-FAMILY TO A BEM
SYSTEM 39 4. SOME PROPERTIES OF BEM SYSTEMS 46 5. NOTES 48 CHAPTER 4.
SUPERPROCESSES 49 1. DEFINITION AND THE FIRST RESULTS 49 2.
SUPERPROCESSES AS LIMITS OF BRANCHING PARTICLE SYSTEMS 53 3. DIRECT
CONSTRUCTION OF SUPERPROCESSES 54 4. SUPPLEMENT TO THE DEFINITION OF A
SUPERPROCESS 58 5. GRAPH OF X 60 6. NOTES 64 CHAPTER 5. SEMILINEAR
PARABOLIC EQUATIONS AND SUPERDIFFUSIONS 67 1. INTRODUCTION 67 2.
CONNECTIONS BETWEEN DIFFERENTIAL AND INTEGRAL EQUATIONS 68 3. ABSOLUTE
BARRIERS 70 4. OPERATORS VQ 75 5. BOUNDARY VALUE PROBLEMS 78 6. NOTES
81 VI CONTENTS PART 2. ELLIPTIC EQUATIONS AND DIFFUSIONS 83 CHAPTER 6.
LINEAR ELLIPTIC EQUATIONS AND DIFFUSIONS 85 1. BASIC FACTS ON SECOND
ORDER ELLIPTIC EQUATIONS 85 2. TIME HOMOGENEOUS DIFFUSIONS 90 3.
PROBABILISTIC SOLUTION OF EQUATION LU = AU 94 4. NOTES 96 CHAPTER 7.
POSITIVE HARMONIC FUNCTIONS 97 1. MARTIN BOUNDARY 97 2. THE EXISTENCE OF
AN EXIT POINT ^_ ON THE MARTIN BOUNDARY 99 3. H-TRANSFORM 102 4.
INTEGRAL REPRESENTATION OF POSITIVE HARMONIC FUNCTIONS 103 5. EXTREME
ELEMENTS AND THE TAIL CR-ALGEBRA 106 6. NOTES 107 CHAPTER 8. MODERATE
SOLUTIONS OF LU = IP(U) 109 1. INTRODUCTION 109 2. FROM PARABOLIC TO
ELLIPTIC SETTING 109 3. MODERATE SOLUTIONS 113 4. SWEEPING OF SOLUTIONS
116 5. LATTICE STRUCTURE OF U 118 6. NOTES 121 CHAPTER 9. STOCHASTIC
BOUNDARY VALUES OF SOLUTIONS 123 1. STOCHASTIC BOUNDARY VALUES AND
POTENTIALS 123 2. CLASSES 3I AND 3 0 126 3. A RELATION BETWEEN
SUPERDIFFUSIONS AND CONDITIONAL DIFFUSIONS 128 4. NOTES 130 CHAPTER 10.
ROUGH TRACE 131 1. DEFINITION AND PRELIMINARY DISCUSSION 131 2.
CHARACTERIZATION OF TRACES 135 3. SOLUTIONS WB WITH BOREL B 137 4. NOTES
141 CHAPTER 11. FINE TRACE 143 1. SINGULARITY SET SG{U) 143 2. CONVEXITY
PROPERTIES OF VB 145 3. FUNCTIONS J U 146 4. PROPERTIES OF SG(U) 150 5.
FINE TOPOLOGY IN E 151 6. AUXILIARY PROPOSITIONS 152 7. FINE TRACE 153
8. ON SOLUTIONS WO 155 9. NOTES 156 CHAPTER 12. MARTIN CAPACITY AND
CLASSES M AND AF 0 157 1. MARTIN CAPACITY 157 2. AUXILIARY PROPOSITIONS
158 3. PROOF OF THE MAIN THEOREM 160 CONTENTS VII 4. NOTES 162 CHAPTER
13. NULL SETS AND POLAR SETS 163 1. NULL SETS 163 2. ACTION OF
DIFFEOMORPHISMS ON NULL SETS 165 3. SUPERCRITICAL AND SUBCRITICAL VALUES
OF A 167 4. NULL SETS AND POLAR SETS 169 5. DUAL DEFINITIONS OF
CAPACITIES 172 6. TRUNCATING SEQUENCES 174 7. PROOF OF THE PRINCIPAL
RESULTS 182 8. NOTES 188 CHAPTER 14. SURVEY OF RELATED RESULTS 193 1.
BRANCHING MEASURE-VALUED PROCESSES 193 2. ADDITIVE FUNCTIONALS 195 3.
PATH PROPERTIES OF THE DAWSON-WATANABE SUPERPROCESS 197 4. A MORE
GENERAL OPERATOR L 198 5. EQUATION LU = -TP(U) 199 6. EQUILIBRIUM
MEASURES FOR SUPERDIFFUSIONS 199 7. MOMENTS OF HIGHER ORDER 201 8.
MARTINGALE APPROACH TO SUPERDIFFUSIONS 203 9. EXCESSIVE FUNCTIONS FOR
SUPERDIFFUSIONS AND THE CORRESPONDING /I-TRANSFORMS 204 10. INFINITE
DIVISIBILITY AND THE POISSON REPRESENTATION 205 11. HISTORICAL
SUPERPROCESSES AND SNAKES 207 APPENDIX A. BASIC FACTS ON MARKOV
PROCESSES AND MARTINGALES 209 1. MULTIPLICATIVE SYSTEMS THEOREM 209 2.
STOPPING TIMES 210 3. MARKOV PROCESSES 210 4. MARTINGALES 214 APPENDIX
B. FACTS ON ELLIPTIC DIFFERENTIAL EQUATIONS 217 1. INTRODUCTION 217 2.
THE BRANDT AND SCHAUDER ESTIMATES 217 3. UPPER BOUND FOR THE POISSON
KERNEL 218 EPILOGUE 221 1. A-MODERATE SOLUTIONS 221 2. EXCEPTIONAL
BOUNDARY SETS 221 3. EXIT BOUNDARY FOR A SUPERDIFFUSION 222 BIBLIOGRAPHY
225 SUBJECT INDEX . 233 NOTATION INDEX 235
|
| any_adam_object | 1 |
| author | Dynkin, Evgenij B. 1924-2014 |
| author_GND | (DE-588)119202085 |
| author_facet | Dynkin, Evgenij B. 1924-2014 |
| author_role | aut |
| author_sort | Dynkin, Evgenij B. 1924-2014 |
| author_variant | e b d eb ebd |
| building | Verbundindex |
| bvnumber | BV014185951 |
| classification_rvk | SK 540 SK 560 SK 820 |
| ctrlnum | (OCoLC)440611138 (DE-599)BVBBV014185951 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:12Z |
| institution | BVB |
| isbn | 0821831747 |
| language | English |
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| series2 | American Mathematical Society Colloquium publications |
| spelling | Dynkin, Evgenij B. 1924-2014 Verfasser (DE-588)119202085 aut Diffusions, superdiffusions and partial differential equations E. B. Dynkin Providence, Rhode Island American Mathematical Society 2002 © 2002 XI, 236 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier American Mathematical Society Colloquium publications volume 50 Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 s Elliptische Differentialgleichung (DE-588)4014485-9 s Parabolische Differentialgleichung (DE-588)4173245-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3196-9 American Mathematical Society Colloquium publications volume 50 (DE-604)BV035417609 50 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009723650&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dynkin, Evgenij B. 1924-2014 Diffusions, superdiffusions and partial differential equations American Mathematical Society Colloquium publications Diffusionsprozess (DE-588)4274463-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4274463-5 (DE-588)4014485-9 (DE-588)4173245-5 |
| title | Diffusions, superdiffusions and partial differential equations |
| title_auth | Diffusions, superdiffusions and partial differential equations |
| title_exact_search | Diffusions, superdiffusions and partial differential equations |
| title_full | Diffusions, superdiffusions and partial differential equations E. B. Dynkin |
| title_fullStr | Diffusions, superdiffusions and partial differential equations E. B. Dynkin |
| title_full_unstemmed | Diffusions, superdiffusions and partial differential equations E. B. Dynkin |
| title_short | Diffusions, superdiffusions and partial differential equations |
| title_sort | diffusions superdiffusions and partial differential equations |
| topic | Diffusionsprozess (DE-588)4274463-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Diffusionsprozess Elliptische Differentialgleichung Parabolische Differentialgleichung |
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