The extended stochastic integral in linear spaces with differentiable measures and related topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 257 S. |
| ISBN: | 9810225687 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | THE EXTENDED STOCHASTIC INTEGRAL IN LINEAR SPACES WITH DIFFERENTIABLE
MEASURES AND RELATED TOPICS NICOLAI VICTOROVICH NORIN MOSCOW INSTITUTE
OF RADIO ENGINEERING, ELECTRONICS AND AUTOMATION MOSCOW, RUSSIA WORLD
SCIENTIFIC SINGAPORE * NEW JERSEY LONDON * HONG KONG CONTENTS PREFACE
STOCHASTIC CALCULUS IN WIENER SPACE 1 1.1 BASIC NOTIONS. ITO INTEGRAL IN
C[0,1] 1 1.1.1 MULTIPLE STOCHASTIC INTEGRAL 6 1.1.2 HERMITE POLYNOMIALS
AND MULTIPLE STOCHASTIC INTEGRALS . . ... 8 1.2 ITO S FORMULA FOR
STOCHASTIC INTEGRAL 13 1.3 BIBLIOGRAPHICAL REMARKS 13 EXTENDED
STOCHASTIC INTEGRAL IN WIENER SPACE 15 2.1- BASIC DEFINITIONS 15 2.2
LOCAL PROPERTIES OF STOCHASTIC DERIVATIVE AND ESI 25 2.3 EXTENDED
STOCHASTIC INTEGRAL WITH VARIABLE UPPER LIMIT 28 2.4 ITO S FORMULA FOR
THE EXTENDED STOCHASTIC INTEGRAL 30 2.5 BIBLIOGRAPHICAL REMARKS 31
RANDOMIZED EXTENDED STOCHASTIC INTEGRALS WITH JUMPS 33 3.1 INTRODUCTION
33 3.2 RANDOMIZED ESI AND ITS CONTINUITY 33 3.3 QUADRATIC VARIATION 37
3.4 ITO S FORMULA 47 3.4.1 ITO S FORMULA FOR RANDOMIZED ESI WITHOUT
JUMPS 47 3.4.2 ITO S FORMULA FOR JUMP DISCONTINUOUS RANDOMIZED ESI 55
3.4.3 SPECIAL CASES OF ITO S FORMULA AND SOME EXAMPLES 57 3.4.4
MULTIDIMENSIONAL ITO S FORMULA 59 3.4.5 THE PROBABILISTIC SOLUTION OF
SOME INTEGRO-DIFFERENTIAL EQUATION 60 3.5 FORMULA FOR BROWNIAN PARTIAL
DERIVATIVES 61 3.6 BIBLIOGRAPHICAL REMARKS 64 INTRODUCTION TO THE THEORY
OF DIFFERENTIABLE MEASURES 65 4.1 MEASURES IN LOCALLY CONVEX SPACES 65
4.2 DEFINITION OF DIFFERENTIABLE MEASURE 67 4.3 DIFFERENTIABILITY OF
GAUSSIAN MEASURE 78 4.4 THE EXTENDED STOCHASTIC INTEGRAL FOR THE WIENER
MEASURE AS THE DIFFERENTIABLE MEASURE 83 4.5 BIBLIOGRAPHICAL REMARKS 85
IX CONTENTS EXTENDED VECTOR STOCHASTIC INTEGRAL IN SOBOLEV SPACES OF
WIENER FUNCTIONALS 87 5.1 INTRODUCTION 87 5.2 ITO-WIENER DECOMPOSITION
FOR GAUSSIAN MEASURE 87 5.3 SOBOLEV SPACES OF WIENER FUNCTIONALS 93 5.4
THE VECTOR EXTENDED STOCHASTIC INTEGRAL 96 5.5 THE ESI IN HILBERT SPACE
OF GENERALIZED FUNCTIONS 106 5.6 QUADRATIC VARIATION OF EXTENDED
STOCHASTIC INTEGRAL IN ABSTRACT WIENER SPACE 114 5.7 BIBLIOGRAPHICAL
REMARKS 120 STOCHASTIC INTEGRALS AND DIFFERENTIABLE MEASURES 121 6.1
INTRODUCTION 121 6.2 MAIN RESULTS 121 6.3 APPLICATIONS 129 6.3.1 THE
IMAGE OF DIFFERENTIABLE MEASURE 129 6.3.2 GAUSS-OSTROGRADSKY FORMULA
130 6.4 SOME FORMULAS FOR DIFFERENTIAL FORMS OF FINITE CODEGREE 131 6.5
BIBLIOGRAPHICAL REMARKS 136 DIFFERENTIAL PROPERTIES OF MIXTURES OF
GAUSSIAN MEASURES 137 7.1 INTRODUCTION 137 7.2 MIXTURES OF GAUSSIAN
MEASURES 138 7.3 THE DIRECT INTEGRAL OF FOCK SPACES 140 7.4 ITO*WIENER
DECOMPOSITION FOR MIXTURES OF GAUSSIAN MEASURES 141 7.5 LOGARITHMIC
DERIVATIVES OF THE MIXTURES OF GAUSSIAN MEASURES . . . . 145 7.6
EXTENDED STOCHASTIC INTEGRAL FOR MIXTURES OF GAUSSIAN MEASURES . . . 147
7.7 ORNSTEIN-UHLENBECK SEMI-GROUP 151 7.8 COMMUTATION RELATIONS 152 7.9
THE ESI IN HILBERT SPACE OF DISTRIBUTIONS 154 7.10 BIBLIOGRAPHICAL
REMARKS 164 SURFACE MEASURES IN BANACH SPACE 165 8.1 THE MEASURE
DERIVATIVES AND TRANSITION MEASURES 165 8.2 SURFACE MEASURES 168 8.3
ALGEBRAIC PROPERTIES OF MAPPING /I I* F/P 173 8.4 DIFFERENTIATION OF
SURFACE MEASURES 176 8.5 APPROXIMATION OF SURFACE MEASURES BY VOLUME
MEASURES 181 8.6 ON INTEGRABILITY OF SECOND ORDER SURFACES IN BANACH
SPACE 188 8.7 BIBLIOGRAPHICAL REMARKS 191 HEAT POTENTIALS ON HILBERT
SPACE 193 9.1 DEFINITION OF HEAT POTENTIALS 193 9.2 DIFFERENTIAL
PROPERTIES OF HEAT POTENTIALS 200 9.3 ANALYTICITY OF HEAT POTENTIALS 203
9.4 CONTINUITY OF HEAT POTENTIALS 208 CONTENTS XI 9.5 THE THEOREM ON THE
JUMPS OF HEAT POTENTIALS 220 9.6 THE HEAT POTENTIALS AND
(QUASI)CHARACTERISTIC OPERATORS 224 9.6.1 THE DEFINITION OF HEAT MOTION
ON BANACH SPACE 224 9.6.2 HEAT POTENTIALS AND (QUASI)CHARACTERISTIC
OPERATORS 230 9.7 INTEGRAL EQUATIONS IN THEORY OF HEAT POTENTIALS 236
9.8 BIBLIOGRAPHICAL REMARKS 244 BIBLIOGRAPHY 245 INDEX 255
|
| any_adam_object | 1 |
| author | Norin, Nikolaj V. |
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| ctrlnum | (OCoLC)34545500 (DE-599)BVBBV011170675 |
| 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 | Mathematik |
| format | Book |
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| id | DE-604.BV011170675 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:10Z |
| institution | BVB |
| isbn | 9810225687 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007489168 |
| oclc_num | 34545500 |
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| physical | XI, 257 S. |
| publishDate | 1996 |
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| publisher | World Scientific |
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| spelling | Norin, Nikolaj V. Verfasser aut The extended stochastic integral in linear spaces with differentiable measures and related topics Nicolai Victorovich Norin Singapore [u.a.] World Scientific 1996 XI, 257 S. txt rdacontent n rdamedia nc rdacarrier Function spaces Stochastic integrals Funktionenraum (DE-588)4134834-5 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s Funktionenraum (DE-588)4134834-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007489168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Norin, Nikolaj V. The extended stochastic integral in linear spaces with differentiable measures and related topics Function spaces Stochastic integrals Funktionenraum (DE-588)4134834-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4134834-5 (DE-588)4126478-2 |
| title | The extended stochastic integral in linear spaces with differentiable measures and related topics |
| title_auth | The extended stochastic integral in linear spaces with differentiable measures and related topics |
| title_exact_search | The extended stochastic integral in linear spaces with differentiable measures and related topics |
| title_full | The extended stochastic integral in linear spaces with differentiable measures and related topics Nicolai Victorovich Norin |
| title_fullStr | The extended stochastic integral in linear spaces with differentiable measures and related topics Nicolai Victorovich Norin |
| title_full_unstemmed | The extended stochastic integral in linear spaces with differentiable measures and related topics Nicolai Victorovich Norin |
| title_short | The extended stochastic integral in linear spaces with differentiable measures and related topics |
| title_sort | the extended stochastic integral in linear spaces with differentiable measures and related topics |
| topic | Function spaces Stochastic integrals Funktionenraum (DE-588)4134834-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Function spaces Stochastic integrals Funktionenraum Stochastisches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007489168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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