An innovation approach to random fields application of white noise theory
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| Format: | Buch |
| Sprache: | English |
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New Jersey [u.a.]
World Scientific
2004
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Datensatz im Suchindex
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| adam_text | AN INNOVATION APPLICATION OF APPROACH TO WHITE NOISE THEORY RANDOM
FIELDS TAKEYUKI HIDA MEIJO UNIVERSITY, JAPAN SI SI AICHI PREFECTURAL
UNIVERSITY, JAPAN WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE *
BEIJING * S H A N G H A I * H O N G K O N G * TAIPEI * CHENNAI CONTENTS
PREFACE VII 1. INTRODUCTION 1 1.1 THE IDEA OF OUR APPROACH 1 1.2 RANDOM
FUNCTIONALS X(C) DEPENDING ON A MANIFOLD C . . . 2 1.3 STOCHASTIC
VARIATIONAL EQUATIONS 6 1.4 RANDOM FUNCTIONS X(F) 7 2. WHITE NOISE 11
2.1 PRELIMINARIES 11 2.2 MULTI-DIMENSIONAL PARAMETER WHITE NOISE 20 2.3
INFINITE DIMENSIONAL ROTATION GROUP O(E) 24 2.4 SUBGROUPS OF O(E) 26 2.5
LAPLACIANS 31 2:6 INVARIANCE OF WHITE NOISE 31 3. POISSON NOISE 33 3.1
POISSON NOISE FUNCTIONALS 33 3.2 FUNCTIONAL EQUATIONS FOR CP(,) 37 3.3
OBSERVATION OF 1-DIMENSIONAL PARAMETER POISSON NOISE ... 39 3.4
CONSTRUCTION OF 1-DIMENSIONAL POISSON NOISE 41 3.5 CONSTRUCTION OF
D-DIMENSIONAL PARAMETER POISSON NOISE ... 42 3.6 INVARIANCE OF POISSON
NOISE 47 3.7 MULTI-DIMENSIONAL PARAMETER POISSON SHEET 48 3.8 COMPOUND
POISSON NOISE 49 3.9 THE SPACE (P) 50 XI XII INNOVATION APPROACH TO
RANDOM FIELDS 4. RANDOM FIELDS 55 4.1 PROCESSES AND FIELDS AS WHITE
NOISE FUNCTIONALS 55 4.2 RANDOM FIELDS X(A) AND X(F) 56 4.3 WHITE NOISE
PARAMETERIZED BY A POINT OF A MANIFOLD . . . . 59 4.4 RANDOM FIELDS
PARAMETERIZED BY A MANIFOLD C 60 4.5 RANDOM FIELDS AS WHITE NOISE
FUNCTIONALS 63 4.6 RANDOM FIELDS AS POISSON NOISE FUNCTIONALS 64 5.
GAUSSIAN RANDOM FIELDS 65 5.1 A REVIEW OF THE CANONICAL REPRESENTATIONS
OF GAUSSIAN PROCESSES 65 5.2 CANONICAL REPRESENTATIONS OF GAUSSIAN
RANDOM FIELDS . . . . 66 5.3 MARTINGALE 72 5.4 A REVIEW OF MARKOV
PROPERTY OF GAUSSIAN PROCESSES 73 5.5 MARKOV PROPERTY OF GAUSSIAN RANDOM
FIELDS 77 5.6 EUCLIDEAN FREE FIELD 82 6. SOME NON-GAUSSIAN RANDOM FIELDS
85 6.1 FIELDS OF HOMOGENEOUS CHAOS 85 6.2 MULTIPLE MARKOV PROPERTIES OF
HOMOGENEOUS CHAOS X(C) 87 6.3 THE POISSON CASE 89 6.4 POISSON NOISE
FUNCTIONALS 93 6.5 RANDOM FIELDS AS POISSON NOISE FUNCTIONALS 94 7.
VARIATIONAL CALCULUS FOR RANDOM FIELDS 97 7.1 GENERALIZED WHITE NOISE
FUNCTIONALS AND RANDOM FIELDS ... 97 .7.2 RESTRICTION OF PARAMETER
(CONTINUED) 98 7.3 VARIATIONAL FORMULA FOR X(C) 99 7.4 VARIATIONAL
EQUATION 103 7.5 EXISTENCE THEOREM FOR A VARIATIONAL EQUATION 105 7.6 A
GENERALIZATION OF THE ITO FORMULA FOR GAUSSIAN RANDOM FIELDS 108 7.7 THE
POISSON CASE 110 7.8 CHARACTERISTIC FUNCTIONALS 112 8. INNOVATION
APPROACH 117 8.1 CONCEPT OF INNOVATION 117 8.2 LEVY DECOMPOSITION OF
INNOVATION 120 8.3 REVIEW OF LINEAR PARAMETER CASE 121 CONTENTS XIII 8.4
INNOVATIONS OF LINEAR PROCESSES 126 8.5 INNOVATION OF A LINEAR RANDOM
FIELD 127 8.6 STOCHASTIC VARIATIONAL EQUATIONS 129 8.7 EXAMPLES 134 9.
REVERSIBILITY 143 9.1 REVERSIBILITY OF STOCHASTIC PROCESSES 143 9.2
REVERSIBILITY OF A RANDOM FIELD 146 9.3 VARIATIONAL EQUATIONS FOR
QUANTUM FIELDS 149 10. APPLICATIONS 151 10.1 CONFORMAL GROUP C(D) AS A
SUBGROUP OF O(E) 151 10.2 SPECTRAL TYPE OF FLOWS 153 10.3 THE
TRANSVERSAL RELATION 155 10.4 CONFORMAL INVARIANCE OF WHITE NOISE 156
10.5 ACTION ON RANDOM FIELDS 156 10.6 MATHEMATICAL BIOLOGY 160 10.7
TOMONAGA-SCHWINGER EQUATION 161 APPENDIX 163 A.I APPENDIX 1 163 A.2
APPENDIX 2 167 A.3 APPENDIX 3 171 A.4 APPENDIX 4 175 EPILOGUE 177 LIST
OF NOTATIONS 179 BIBLIOGRAPHY 181 INDEX 187
|
| any_adam_object | 1 |
| author | Hida, Takeyuki 1927-2017 Si, Si |
| author_GND | (DE-588)124605257 (DE-588)1168187079 |
| author_facet | Hida, Takeyuki 1927-2017 Si, Si |
| author_role | aut aut |
| author_sort | Hida, Takeyuki 1927-2017 |
| author_variant | t h th s s ss |
| building | Verbundindex |
| bvnumber | BV017403654 |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)248552156 (DE-599)BVBBV017403654 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017403654 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:26:05Z |
| institution | BVB |
| isbn | 9812380957 |
| language | English |
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| physical | XIII, 189 S. Illustrationen |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Hida, Takeyuki 1927-2017 Si, Si An innovation approach to random fields application of white noise theory Weißes Rauschen (DE-588)4189502-2 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| subject_GND | (DE-588)4189502-2 (DE-588)4191094-1 |
| title | An innovation approach to random fields application of white noise theory |
| title_auth | An innovation approach to random fields application of white noise theory |
| title_exact_search | An innovation approach to random fields application of white noise theory |
| title_full | An innovation approach to random fields application of white noise theory Takeyuki Hida ; Si Si |
| title_fullStr | An innovation approach to random fields application of white noise theory Takeyuki Hida ; Si Si |
| title_full_unstemmed | An innovation approach to random fields application of white noise theory Takeyuki Hida ; Si Si |
| title_short | An innovation approach to random fields |
| title_sort | an innovation approach to random fields application of white noise theory |
| title_sub | application of white noise theory |
| topic | Weißes Rauschen (DE-588)4189502-2 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| topic_facet | Weißes Rauschen Zufälliges Feld |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010487751&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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