Introduction to infinite dimensional stochastic analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Dortrecht [u.a.]
Kluwer [u.a.]
2000
|
| Series: | Mathematics and its applications
502 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 296 S. |
| ISBN: | 079236208X 1880132583 7030078187 |
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Record in the Search Index
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| adam_text | INTRODUCTION TO INFINITE DIMENSIONAL STOCHASTIC ANALYSIS BY ZHI*YUAN
HUANG DEPARTMENT OF MATHEMATICS, HUAZHONG UNIVERSITY OF SCIENCE AND
TECHNOLOGY, WUHAN P. R. CHINA AND JIA*AN YAN INSTITUTE OF APPLIED
MATHEMATICS, CHINESE ACADEMY OF SCIENCES, BEIJING P. R. CHINA. ILLL TF
SCIENCE PRESS BEIJING/NEW YORK, KLUWER ACADEMIC PUBLISHERS
DORDRECHT/BOSTON/LONDON CONTENTS PREFACE IX CHAPTER I FOUNDATIONS OF
INFINITE DIMENSIONAL ANALYSIS 1 §1. LINEAR OPERATORS ON HILBERT SPACES 1
1.1 BASIC NOTIONS, NOTATIONS AND LEMMAS 1 1.2 CLOSABLE, SYMMETRIC AND
SELF-ADJOINT OPERATORS 4 1.3 SELF-ADJOINT EXTENSION OF A SYMMETRIC
BOUNDED BELOW OPERATOR ... 8 1.4 SPECTRAL RESOLUTION OF SELF-ADJOINT
OPERATORS 10 1.5 HILBERT-SCHMIDT AND TRACE CLASS OPERATORS 14 §2. FOCK
SPACES AND SECOND QUANTIZATION 19 2.1 TENSOR PRODUCTS OF HILBERT SPACES
19 2.2 FOCK SPACES 24 2.3 SECOND QUANTIZATION OF OPERATORS 26 §3.
COUNTABLY NORMED SPACES AND NUCLEAR SPACES 29 3.1 COUNTABLY NORMED
SPACES AND THEIR DUAL SPACES 30 3.2 NUCLEAR SPACES AND THEIR DUAL SPACES
34 3.3 TOPOLOGICAL TENSOR PRODUCT, THE SCHWARTZ KERNELS THEOREM 38 §4.
BOREL MEASURES ON TOPOLOGICAL LINEAR SPACES 41 4.1 MINLOS-SAZANOV
THEOREM 41 4.2 GAUSSIAN MEASURES ON HILBERT SPACES 48 4.3 GAUSSIAN
MEASURES ON BANACH SPACES 51 CHAPTER II MALLIAVIN CALCULUS 59 §1.
GAUSSIAN PROBABILITY SPACES AND WIENER CHAOS DECOMPOSITION 59 1.1
FUNCTIONAL ON GAUSSIAN PROBABILITY SPACES 59 1.2 NUMERICAL MODELS 64 1.3
MULTIPLE WIENER-ITO INTEGRAL REPRESENTATION 67 §2. DIFFERENTIAL CALCULUS
OF FUNCTIONALS, GRADIENT AND DIVERGENCE OPERATORS 72 2.1 FINITE
DIMENSIONAL GAUSSIAN PROBABILITY SPACES 72 2.2 GRADIENT AND DIVERGENCE
OF SMOOTH FUNCTIONALS 76 2.3 SOBOLEV SPACES OF FUNCTIONALS 81 §3.
MEYER S INEQUALITIES AND SOME CONSEQUENCES 86 3.1 OMSTEIN-UHLENBECK
SEMIGROUP 86 VI CONTENTS 3.2 Z, P -MULTIPLIER THEOREM 89 3.3 MEYER S
INEQUALITIES 92 3.4~MEYER-WATANABE S GENERALIZED FUNCTIONALS 97 §4.
DENSITIES OF NON-DEGENERATE FUNCTIONALS 100 4.1 MALLIAVIN COVARIANCE
MATRICES, SOME LEMMAS 101 4.2 EXISTENCE OF DENSITIES : 103 4.3
SMOOTHNESS OF DENSITIES 106 4.4 EXAMPLES 110 CHAPTER III STOCHASTIC
CALCULUS OF VARIATION FOR WIENER FUNCTIONALS 113 §1. DIFFERENTIAL
CALCULUS OF LTD FUNCTIONALS AND REGULARITY OF HEAT KERNELS 113 1.1
SKOROHOD INTEGRALS 113 1.2 SMOOTHNESS OF SOLUTIONS TO STOCHASTIC
DIFFERENTIAL EQUATIONS 118 1.3 HYPOELLIPTICITY AND HORMANDER S
CONDITIONS 120 1.4 A PROBABILISTIC PROOF OF HORMANDER S THEOREM 125 §2.
POTENTIAL THEORY OVER WIENER SPACES AND QUASI-SURE ANALYSIS 130 2.1
(FC,P)-CAPACITIES 130 2.2 QUASI-CONTINUOUS MODIFICATIONS 133 2.3
TIGHTNESS, CONTINUITY AND INVARIANCE OF CAPACITIES 135 2.4 POSITIVE
GENERALIZED FUNCTIONALS AND MEASURES WITH FINITE ENERGY 139 2.5 SOME
QUASI-SURE SAMPLE PROPERTIES OF STOCHASTIC PROCESSES 142 §3.
ANTICIPATING STOCHASTIC CALCULUS 145 3.1 APPROXIMATION OF SKOROHOD
INTEGRALS BY RIEMANNIAN SUMS 145 3.2 ITO FORMULA FOR ANTICIPATING
PROCESSES 149 3.3 ANTICIPATING STOCHASTIC DIFFERENTIAL EQUATIONS 155
CHAPTER IV GENERAL THEORY OF WHITE NOISE ANALYSIS 161 §1. GENERAL
FRAMEWORK FOR WHITE NOISE ANALYSIS 162 1.1 WICK TENSOR PRODUCTS AND THE
WIENER-ITO-SEGAL ISOMORPHISM .. 162 1.2 TESTING FUNCTIONAL SPACE AND
DISTRIBUTION SPACE .. *. 165 1.3 CLASSICAL FRAMEWORK FOR WHITE NOISE
ANALYSIS 169 §2. CHARACTERIZATION OF FUNCTIONAL SPACES 171 2.1
S-TRANSFORM AND CHARACTERIZATION OF SPACE (B)~ /3 (O /3 2.2 LOCAL
S-TRANSFORM AND CHARACTERIZATION OF SPACE (E)^. 1 177 2.3 TWO
CHARACTERIZATIONS FOR TESTING FUNCTIONAL SPACES 179 2.4 SOME EXAMPLES OF
DISTRIBUTIONS 183 CONTENTS VII §3. PRODUCTS AND WICK PRODUCTS OF
FUNCTIONALS 188 3.1 PRODUCTS OF FUNCTIONALS 188 3.2 WICK PRODUCTSOF
DISTRIBUTIONS 191 3.3 APPLICATION TO FEYNMAN INTEGRALS 193 §4. MOMENT
CHARACTERIZATION OF DISTRIBUTIONS AND POSITIVE DISTRIBUTIONS 195 4.1 THE
RENORMALIZATION OPERATOR 195 4.2 MOMENT CHARACTERIZATION OF DISTRIBUTION
SPACES 197 4.3 MEASURE REPRESENTATION OF POSITIVE DISTRIBUTIONS 199 4.4
APPLICATION TO P(0) 2 -QUANTUM FIELDS 206 CHAPTER V LINEAR OPERATORS ON
DISTRIBUTION SPACES 210 §1. ANALYTIC CALCULUS FOR DISTRIBUTIONS 210 1.1
SCALING TRANSFORMATIONS 210 1.2 SHIFT OPERATORS AND SOBOLEV
DIFFERENTIATIONS 212 1.3 GRADIENT AND DIVERGENCE OPERATORS 216 §2.
CONTINUOUS LINEAR OPERATORS ON DISTRIBUTION SPACES 219 2.1 SYMBOLS AND
CHAOS DECOMPOSITIONS FOR OPERATORS 219 2.2 S-TRANSFORMS AND WICK
PRODUCTS OF GENERALIZED OPERATORS 224 §3. INTEGRAL KERNEL OPERATORS AND
INTEGRAL KERNEL REPRESENTATION FOR OPERATORS 229 3.1 CONTRACTION OF
TENSOR PRODUCTS 229 3.2 INTEGRAL KERNEL OPERATORS 231 3.3 INTEGRAL
KERNEL REPRESENTATION FOR GENERALIZED OPERATORS 237 §4. APPLICATIONS TO
QUANTUM PHYSICS 240 4.1 QUANTUM STOCHASTIC INTEGRALS 240 4.2
KLEIN-GORDON FIELD 243 4.3 INFINITE DIMENSIONAL CLASSICAL DIRICHLET
FORMS 245 APPENDIX A HERMITE POLYNOMIALS AND HERMITE FUNCTIONS 252
APPENDIX B LOCALLY CONVEX SPACES AND THEIR DUAL SPACES 257 1.
SEMI-NORMS, NORMS AND H-NORMS 257 2. LOCALLY CONVEX TOPOLOGICAL LINEAR
SPACES, BOUNDED SETS 258 3. PROJECTIVE TOPOLOGIES AND PROJECTIVE LIMITS
259 4. INDUCTIVE TOPOLOGIES AND INDUCTIVE LIMITS 260 5. DUAL SPACES AND
WEAK TOPOLOGIES 261 6. COMPATIBILITY AND MACKEY TOPOLOGY 262 7. STRONG
TOPOLOGIES AND REFLEXIVITY 263 VLLL CONTENTS 8. DUAL MAPS 263 9.
UNIFORMLY CONVEX SPACES AND BANACH-SAKS THEOREM 264 COMMENTS 266
REFERENCES 271 SUBJECT INDEX 290 INDEX OF SYMBOLS 294
|
| any_adam_object | 1 |
| author | Huang, Zhi-yuan Yan, Jia-an 1941- |
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| dewey-search | 519.2 |
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| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:45:46Z |
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| language | English Chinese |
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| physical | XI, 296 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Kluwer [u.a.] |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Huang, Zhi-yuan Verfasser aut Introduction to infinite dimensional stochastic analysis by Zhi-yuan Huang and Jia-an Yan Dortrecht [u.a.] Kluwer [u.a.] 2000 XI, 296 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 502 Function spaces Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 s DE-604 Yan, Jia-an 1941- Verfasser (DE-588)1031504184 aut Mathematics and its applications 502 (DE-604)BV008163334 502 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009165646&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huang, Zhi-yuan Yan, Jia-an 1941- Introduction to infinite dimensional stochastic analysis Mathematics and its applications Function spaces Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4132272-1 |
| title | Introduction to infinite dimensional stochastic analysis |
| title_auth | Introduction to infinite dimensional stochastic analysis |
| title_exact_search | Introduction to infinite dimensional stochastic analysis |
| title_full | Introduction to infinite dimensional stochastic analysis by Zhi-yuan Huang and Jia-an Yan |
| title_fullStr | Introduction to infinite dimensional stochastic analysis by Zhi-yuan Huang and Jia-an Yan |
| title_full_unstemmed | Introduction to infinite dimensional stochastic analysis by Zhi-yuan Huang and Jia-an Yan |
| title_short | Introduction to infinite dimensional stochastic analysis |
| title_sort | introduction to infinite dimensional stochastic analysis |
| topic | Function spaces Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Function spaces Stochastic analysis Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009165646&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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