White noise distribution theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1996
|
| Schriftenreihe: | Probability and stochastics series
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | [11], 378 S. |
| ISBN: | 0849380774 |
Internformat
MARC
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| 490 | 0 | |a Probability and stochastics series | |
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Datensatz im Suchindex
| _version_ | 1804125507664478208 |
|---|---|
| adam_text | Contents
^ 1 Introduction to White Noise 1
1.1 What is white noise? 1
1.2 A simple example 2
2 Background 7
2.1 Abstract Wiener spaces 7
2.2 Countably Hilbert spaces 9
2.3 Nuclear spaces 11
2.4 Gel fand triples 12
3 White Noise as an Infinite Dimensional Calculus 15
3.1 White noise space 15
3.2 A reconstruction of the Schwartz space 17
3.3 The spaces of test and generalized functions 18
3.4 Some examples of test and generalized functions 21
.• 4 Constructions of Test and Generalized Functions 23
4.1 General ideas for several constructions 23
4.2 Construction from a Hilbert space and an operator .... 25
4.3 General construction of Kubo and Takenaka 27
4.4 Construction of Kondratiev and Streit 29
5 The S transform 31
5.1 Wick tensors and multiple Wiener integrals 32
5.2 Definition of the 5 transform 36
5.3 Examples of generalized functions 40
6 Continuous Versions and Analytic Extensions 45
6.1 Continuous versions of test functions 45
6.2 Growth condition and norm estimates 54
6.3 Analytic extensions of test functions 57
7 Delta Functions 61
7.1 Donsker s delta function 61
7.2 Kubo Yokoi delta function 67
7.3 Continuity of the delta functions 72
Contents
J8 Characterization Theorems 77
8.1 Characterization of generalized functions 77
8.2 Convergence of generalized functions 86
8.3 Characterization of test functions 89
8.4 Wick product and convolution 92
8.5 Integrable functions 99
9 Differential Operators 103
9.1 Differential operators 103
9.2 Adjoint operators 110
9.3 Multiplication operators 113
9.4 Gross differentiation and gradient 116
10 Integral Kernel Operators 121
10.1 Heuristic discussion 121
10.2 Integral kernel operators 123
10.3 Gross Laplacian and number operator 130
10.4 Lambda operator 136
10.5 Translation operators 138
10.6 Representation theorem 143
11 Fourier Transforms 147
11.1 Definition of the Fourier transform 147
11.2 Representations of the Fourier transform 153
11.3 Basic properties 155
11.4 Decomposition of the Fourier transform 162
11.5 Fourier Gauss transforms 164
11.6 Characterization of the Fourier transform 174
11.7 Fourier Mehler transforms 177
11.8 Initial value problems 184
12 Laplacian Operators 189
12.1 Semigroup for the Gross Laplacian 189
12.2 Semigroup for the number operator 194
12.3 Levy Laplacian 199
12.4 Levy Laplacian by the 5 transform 206
12.5 Spherical mean and the Levy Laplacian 213
12.6 Relationship between Gross and Levy Laplacians .... 218
12.7 Volterra Laplacian 224
12.8 Relationships with the Fourier transform 230
12.9 Two dimensional rotations 232
13 White Noise Integration 239
13.1 Informal motivation 239
13.2 Pettis and Bochner integrals 241
13.3 White noise integrals 245
13.4 An extension of the Ito integral 253
Contents
13.5 Generalizations of Ito s formula 264
13.6 One sided white noise differentiation 274
13.7 Stochastic integral equations 279
13.8 White noise integral equations 291
14 Feynman Integrals 305
14.1 Informal derivation 305
14.2 White noise formulation 307
14.3 Explicit calculation 311
15 Positive Generalized Functions 317
15.1 Positive generalized functions 317
15.2 Construction of Lee 326
15.3 Characterization of Hida measures 331
Appendix A: Notes and Comments 335
Appendix B: Miscellaneous Formulas 353
Bibliography 359
List of Symbols 369
Index 373
|
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| author | Kuo, Hui-Hsiung 1941- |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| id | DE-604.BV011018720 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:02:40Z |
| institution | BVB |
| isbn | 0849380774 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007376307 |
| oclc_num | 34473467 |
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| physical | [11], 378 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | CRC Press |
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| series2 | Probability and stochastics series |
| spelling | Kuo, Hui-Hsiung 1941- Verfasser (DE-588)108437809 aut White noise distribution theory Hui-Hsiung Kuo Boca Raton [u.a.] CRC Press 1996 [11], 378 S. txt rdacontent n rdamedia nc rdacarrier Probability and stochastics series Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Wiener-Integral (DE-588)4189867-9 gnd rswk-swf Gaußsches Rauschen (DE-588)4200026-9 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s Weißes Rauschen (DE-588)4189502-2 s DE-604 Gaußsches Rauschen (DE-588)4200026-9 s Wiener-Integral (DE-588)4189867-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007376307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuo, Hui-Hsiung 1941- White noise distribution theory Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Wiener-Integral (DE-588)4189867-9 gnd Gaußsches Rauschen (DE-588)4200026-9 gnd Stochastisches Integral (DE-588)4126478-2 gnd Weißes Rauschen (DE-588)4189502-2 gnd |
| subject_GND | (DE-588)4189867-9 (DE-588)4200026-9 (DE-588)4126478-2 (DE-588)4189502-2 |
| title | White noise distribution theory |
| title_auth | White noise distribution theory |
| title_exact_search | White noise distribution theory |
| title_full | White noise distribution theory Hui-Hsiung Kuo |
| title_fullStr | White noise distribution theory Hui-Hsiung Kuo |
| title_full_unstemmed | White noise distribution theory Hui-Hsiung Kuo |
| title_short | White noise distribution theory |
| title_sort | white noise distribution theory |
| topic | Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Wiener-Integral (DE-588)4189867-9 gnd Gaußsches Rauschen (DE-588)4200026-9 gnd Stochastisches Integral (DE-588)4126478-2 gnd Weißes Rauschen (DE-588)4189502-2 gnd |
| topic_facet | Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Wiener-Integral Gaußsches Rauschen Stochastisches Integral Weißes Rauschen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007376307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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