Diffusions and waves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer Acad. Publ.
2002
|
| Schriftenreihe: | Mathematics and its applications
552 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VIII, 236 S. |
| ISBN: | 1402009674 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | DIFFUSIONS AND WAVES BY HENRYK GZYL KLUWER ACADEMIC PUBLISHERS DORDRECHT
/ BOSTON / LONDON CONTENTS INTRODUCTION , 1 CHAPTER 1. BASIC
PROBABILISTIC NOTIONS 3 1.1. PROBABILITY SPACES 3 1.2. CONDITIONAL
EXPECTATIONS 6 1.3. EXAMPLES OF CONDITIONAL EXPECTATIONS 7 1.4.
PROCESSES 9 1.5. SEMIGROUPS, GENERATORS AND RESOLVENTS 12 1.5.1.
SEMIGROUPS 12 1.5.2. RESOLVENTS 14 1.6. EXAMPLES 15 1.7. CONSTRUCTION OF
MARKOV PROCESSES 17 1.7.1. BASICS 17 1.7.2. SKETCH OF CONSTRUCTIONS 19
1.7.3. STOPPING TIMES AND THE STRONG MARKOV PROPERTY 20 1.8.
TRANSFORMATIONS OF MARKOV PROCESSES * 23 1.8.1. ADDITIVE AND
MULTIPLICATIVE FUNCTIONALS 23 1.8.2. TIME CHANGING A MARKOV PROCESS 26
1.8.3. THE KILLING OF A MARKOV PROCESS 27 REFERENCES 29 CHAPTER 2. FROM
BROWNIAN MOTION TO DIFFUSIONS 31 2.1. BROWNIAN MOTION 31 2.1.1. THE
CLASSICAL APPROACH 31 2.1.2. THE MODERN APPROACH 34 2.1.3. SOME
IMPORTANT HITTING TIMES AND HITTING DISTRIBUTIONS 34 2.1.4. DIRICHLET
PROBLEM FOR THE LAPLACIAN 37 2.2. DIFFUSIONS 39 VI CONTENTS 2.2.1.
STOCHASTIC INTEGRATION WITH RESPECT TO BROWNIAN MOTION 40 2.2.2. THE
CAMERON-MARTIN-GIRSANOV-MARUYAMA TRANSFORMATION 45 2.3. DIFFUSIONS AS
SOLUTIONS OF STOCHASTIC EQUATIONS 46 2.3.1. THE BASIC STOCHASTIC
DIFFERENTIAL EQUATION 47 2.3.2. THE MARKOV NATURE OF THE SOLUTIONS 48
2.4. REFLECTED DIFFUSIONS 49 2.5. KILLED DIFFUSIONS AND SOME FUNDAMENTAL
IDENTITIES 53 REFERENCES 57 CHAPTER 3. WAVES 59 INTRODUCTION 59 3.1.
WAVES OF CONSTANT SPEED IN R D 60 3.1.1. WAVES IN ONE-DIMENSIONAL SPACE
61 3.1.2. WAVES IN SPACES OF DIMENSION D 1: AVERAGING METHODS 62
3.1.3. WAVES IN SPACES OF DIMENSION D 1. THE FOURIER TRANSFORM
APPROACH 65 3.1.4. FOURIER TRANSFORM IN TIME 65 3.1.5. FOURIER TRANSFORM
IN SPACE 67 3.1.6. EXPANSION OF THE SOLUTION IN PLANE WAVES 68 3.1.7.
THE (DE)COMPLEXIFICATION APPROACH 68 3.1.8. FACTORIZATION 69 3.2.
PROPAGATORS AND GREEN FUNCTIONS 72 3.3. GEOMETRICAL OPTICS 77 3.3.1.
BASICS 77 3.3.2. SOLVING THE EIKONAL EQUATION 78 3.3.3. SOLVING THE
TRANSPORT EQUATIONS 81 3.4. GENERAL REPRESENTATION OF SOLUTIONS 83
REFERENCES 87 CHAPTER 4. WAVES AND BROWNIAN MOTIONS 89 4.1. WAVES IN
FULL SPACE 89 4.2. DIRICHLET PROBLEMS 92 4.2.1. WAVES IN HALF SPACE WITH
DIRICHLET BOUNDARY CONDITIONS 93 4.2.2. WAVES IN A SPHERE WITH DIRICHLET
BOUNDARY CONDITIONS 95 4.3. NEUMANN TYPE BOUNDARY CONDITIONS 96 4.4.
EXISTENCE RESULTS 98 4.5. PROBLEMS OF DIRICHLET TYPE IN UNBOUNDED
DOMAINS: FROM THE MARKOV PROPERTY TO THE HUYGENS CONDITION AND THE
SOMMERFELD RADIATION CONDITION 99 4.5.1. THE DIRICHLET PROBLEM IN
UNBOUNDED DOMAINS 99 4.5.2. FROM THE MARKOV PROPERTY TO THE HUYGENS
CONSTRUCTION 100 4.5.3. SOMMERFELD S RADIATION CONDITION 101 4.6.
EXTENDED HADAMARD S CONSTRUCTION 104 4.7. FROM RESOLVENTS TO PROPAGATORS
105 4.8. RECIPROCITY: A PROBABILISTIC APPROACH 107 REFERENCES 110
CONTENTS VII CHAPTER 5. WAVES AND DIFFUSIONS 113 5.1. WAVES IN FULL
SPACE 113 5.2. EXISTENCE OF SOLUTIONS TO THE WAVE EQUATIONS 116 5.3. AN
EVALUATION OF SOME PATH INTEGRALS 118 5.4. WAVES IN STRATIFIED MEDIA 119
5.4.1. WAVES IN A ONE-DIMENSIONAL STRATIFIED MEDIUM 120 5.4.2. WAVES IN
A STRATIFIED HALF-SPACE 123 5.4.3. A CHANGE OF SPATIAL SCALES . 124
5.4.4. WAVES IN MULTIDIMENSIONAL STRATIFIED MEDIA 126 5.4.5. EXAMPLES
127 5.5. MAXENTROPIC EQUIVALENT LINEARIZATION AND APPROXIMATE SOLUTIONS
TO THE WAVE EQUATIONS 130 REFERENCES 133 CHAPTER 6. ASYMPTOTIC
EXPANSIONS / 135 6.1. DIGRESSIVE INTRODUCTION 135 6.2. PROBABILISTIC
APPROACH TO GEOMETRICAL OPTICS 141 6.3. GEOMETRICAL OPTICS AND THE
DIRICHLET PROBLEM 143 6.4. TWO VARIATIONS ON A THEME 145 6.4.1. THE
FIRST VARIATION ON THE THEME 145 6.4.2. THE SECOND VARIATION ON THE
THEME 147 6.5. GEOMETRICAL OPTICS AND THE NEUMANN PROBLEM 148 6.6.
EXAMPLE 149 6.7. LONG TIME ASYMPTOTICS 152 REFERENCES 154 CHAPTER 7.
TRANSMUTATION OPERATIONS 155 7.1. BASIC TRANSMUTATIONS 155 7.2.
PROBABILISTIC VERSION OF TRANSMUTATION OPERATIONS 158 7.3. EXAMPLES 162
7.4. MORE INVERSION TECHNIQUES AND SIMPLE EXAMPLES 165 7.5. THE ASCENT
METHOD 170 7.6. THE CLOSING OF THE CIRCLE. SOME HEURISTICS 174
REFERENCES 175 CHAPTER 8. MORE CONNECTIONS 177 8.1. WAVES IN DISCRETE
STRUCTURES AND MARKOV CHAINS 177 8.2. APPROXIMATE LAPLACIANS, REGULAR
JUMP PROCESSES AND RANDOM FLIGHTS 180 8.2.1. APPROXIMATE LAPLACIANS 180
8.3. REGULAR JUMP PROCESSES 182 8.4. RANDOM FLIGHTS 185 8.5. RANDOM
EVOLUTIONS 187 8.6. FIRST-ORDER HYPERBOLIC SYSTEMS 192 VIII CONTENTS
8.6.1. ONE-DIMENSIONAL STRATIFIED MEDIA A LA GAVEAU 194 8.6.2.
THOMAS COMPLETION OF FEYNMANN S SUGGESTION 19 5 8.7. PSEUDO PROCESSES
AND EULER S EQUATION 198 8.8. DAMPED WAVES: PLAYING WITH A SIMPLE MODEL
201 REFERENCES 206 CHAPTER 9. APPLICATIONS 209 9.1. AN INVERSE SOURCE
PROBLEM * 209 9.1.1. A BASIC RESULT 209 9.1.2. EQUIVALENT SOURCE
PROBLEM 211 9.1.3. SOLVING THE INTEGRAL GEOMETRY PROBLEM 213 9.1.4. SOME
VERY SIMPLE EXAMPLES 215 9.2. PROBABILISTIC APPROACH TO A DISCRETE
INVERSE PROBLEM 217 9.3. DEPENDENCE OF BOUNDARY DATA ON PROPAGATION
VELOCITY 220 9.4. THE BORN APPROXIMATION 221 9.4.1. INVERSION OF THE
BORN APPROXIMATION 224 9.5. SCATTERING BY A BOUNDED OBJECT 228 9.5.1.
POINT SOURCES 231 REFERENCES 234 SUBJECT INDEX 235
|
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| id | DE-604.BV014794466 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:07:14Z |
| institution | BVB |
| isbn | 1402009674 |
| language | English |
| lccn | 2002034392 |
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| physical | VIII, 236 S. |
| publishDate | 2002 |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Gzyl, Henryk 1946- Verfasser (DE-588)172111188 aut Diffusions and waves by Henryk Gzyl Boston [u.a.] Kluwer Acad. Publ. 2002 VIII, 236 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 552 Includes bibliographical references and index Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 s Diffusionsprozess (DE-588)4274463-5 s DE-604 Mathematics and its applications 552 (DE-604)BV008163334 552 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011798&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gzyl, Henryk 1946- Diffusions and waves Mathematics and its applications Diffusionsprozess (DE-588)4274463-5 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| subject_GND | (DE-588)4274463-5 (DE-588)4121912-0 |
| title | Diffusions and waves |
| title_auth | Diffusions and waves |
| title_exact_search | Diffusions and waves |
| title_full | Diffusions and waves by Henryk Gzyl |
| title_fullStr | Diffusions and waves by Henryk Gzyl |
| title_full_unstemmed | Diffusions and waves by Henryk Gzyl |
| title_short | Diffusions and waves |
| title_sort | diffusions and waves |
| topic | Diffusionsprozess (DE-588)4274463-5 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| topic_facet | Diffusionsprozess Wellenausbreitung |
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