The Malliavin calculus and related topics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
[2006]
|
| Edition: | Second edition |
| Series: | Probability and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 382 Seiten |
| ISBN: | 9783540283287 3540283285 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Malliavin calculus and related topics |c David Nualart |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c [2006] | |
| 264 | 4 | |c © 2006 | |
| 300 | |a xiv, 382 Seiten | ||
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Record in the Search Index
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| adam_text | DAVID NUALART THE MALLIAVIN CALCULUS AND RELATED TOPICS ^J SPRINGER
CONTENTS INTRODUCTION 1 1 ANALYSIS ON THE WIENER SPACE 3 1.1 WIENER
CHAOS AND STOCHASTIC INTEGRALS 3 1.1.1 THE WIENER CHAOS DECOMPOSITION 4
1.1.2 THE WHITE NOISE CASE: MULTIPLE WIENER-ITO INTEGRALS . 8 1.1.3 ITO
STOCHASTIC CALCULUS 15 1.2 THE DERIVATIVE OPERATOR 24 1.2.1 THE
DERIVATIVE OPERATOR IN THE WHITE NOISE CASE ... 31 1.3 THE DIVERGENCE
OPERATOR 36 1.3.1 PROPERTIES OF THE DIVERGENCE OPERATOR 37 1.3.2 THE
SKOROHOD INTEGRAL 40 1.3.3 THE ITO STOCHASTIC INTEGRAL AS A PARTICULAR
CASE OF THE SKOROHOD INTEGRAL 44 1.3.4 STOCHASTIC INTEGRAL
REPRESENTATION OF WIENER FUNCTIONALS 46 1.3.5 LOCAL PROPERTIES 47 1.4
THE ORNSTEIN-UHLENBECK SEMIGROUP 54 1.4.1 THE SEMIGROUP OF
ORNSTEIN-UHLENBECK 54 1.4.2 THE GENERATOR OF THE ORNSTEIN-UHLENBECK
SEMIGROUP 58 1.4.3 HYPERCONTRACTIVITY PROPERTY AND THE MULTIPLIER
THEOREM 61 1.5 SOBOLEV SPACES AND THE EQUIVALENCE OF NORMS 67 XII
CONTENTS 2 REGULARITY OF PROBABILITY LAWS 85 2.1 REGULARITY OF DENSITIES
AND RELATED TOPICS 85 2.1.1 COMPUTATION AND ESTIMATION OF PROBABILITY
DENSITIES 86 2.1.2 A CRITERION FOR ABSOLUTE CONTINUITY BASED ON THE
INTEGRATION-BY-PARTS FORMULA 90 2.1.3 ABSOLUTE CONTINUITY USING BOULEAU
AND HIRSCH S AP- PROACH 94 2.1.4 SMOOTHNESS OF DENSITIES 99 2.1.5 .
COMPOSITION OF TEMPERED DISTRIBUTIONS WITH NONDE- GENERATE RANDOM
VECTORS 104 2.1.6 PROPERTIES OF THE SUPPORT OF THE LAW 105 2.1.7
REGULARITY OF THE LAW OF THE MAXIMUM OF CONTINUOUS PROCESSES 108 2.2
STOCHASTIC DIFFERENTIAL EQUATIONS 116 2.2.1 EXISTENCE AND UNIQUENESS OF
SOLUTIONS 117 2.2.2 WEAK DIFFERENTIABILITY OF THE SOLUTION 119 2.3
HYPOELLIPTICITY AND HORMANDER S THEOREM 125 2.3.1 ABSOLUTE CONTINUITY IN
THE CASE OF LIPSCHITZ COEFFICIENTS 125 2.3.2 ABSOLUTE CONTINUITY UNDER
HORMANDER S CONDITIONS . 128 2.3.3 SMOOTHNESS OF THE DENSITY UNDER
HORMANDER S CONDITION 133 2.4 STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
142 2.4.1 STOCHASTIC INTEGRAL EQUATIONS ON THE PLANE 142 2.4.2 ABSOLUTE
CONTINUITY FOR SOLUTIONS TO THE STOCHASTIC HEAT EQUATION 151 3
ANTICIPATING STOCHASTIC CALCULUS 169 3.1 APPROXIMATION OF STOCHASTIC
INTEGRALS 169 3.1.1 STOCHASTIC INTEGRALS DEFINED BY RIEMANN SUMS ....
170 3.1.2 THE APPROACH BASED ON THE L 2 DEVELOPMENT OF THE PROCESS 176
3.2 STOCHASTIC CALCULUS FOR ANTICIPATING INTEGRALS 180 3.2.1 SKOROHOD
INTEGRAL PROCESSES 180 3.2.2 CONTINUITY AND QUADRATIC VARIATION OF THE
SKOROHOD INTEGRAL 181 3.2.3 ITO S FORMULA FOR THE SKOROHOD AND
STRATONOVICH INTEGRALS 184 3.2.4 SUBSTITUTION FORMULAS 195 3.3
ANTICIPATING STOCHASTIC DIFFERENTIAL EQUATIONS 208 3.3.1 STOCHASTIC
DIFFERENTIAL EQUATIONS IN THE SRATONOVICH SENSE 208 3.3.2 STOCHASTIC
DIFFERENTIAL EQUATIONS WITH BOUNDARY CON- DITIONS 215 CONTENTS XIII
3.3.3 STOCHASTIC DIFFERENTIAL EQUATIONS IN THE SKOROHOD SENSE 217
TRANSFORMATIONS OF THE WIENER MEASURE 225 4.1 ANTICIPATING GIRSANOV
THEOREMS 225 4.1.1 THE ADAPTED CASE 226 4.1.2 GENERAL RESULTS ON
ABSOLUTE CONTINUITY OF TRANSFORMATIONS 228 4.1.3 CONTINUOUSLY
DIFFERENTIABLE VARIABLES IN THE DIRECTION OF H 1 230 4.1.4
TRANSFORMATIONS INDUCED BY ELEMENTARY PROCESSES . . 232 4.1.5
ANTICIPATING GIRSANOV THEOREMS 234 4.2 MARKOV RANDOM FIELDS 241 4.2.1
MARKOV FIELD PROPERTY FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH
BOUNDARY CONDITIONS 242 4.2.2 MARKOV FIELD PROPERTY FOR SOLUTIONS TO
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS 249 4.2.3 CONDITIONAL
INDEPENDENCE AND FACTORIZATION PROPERTIES 258 FRACTIONAL BROWNIAN MOTION
273 5.1 DEFINITION, PROPERTIES AND CONSTRUCTION OF THE FRACTIONAL BROWN-
IAN MOTION 273 5.1.1 SEMIMARTINGALE PROPERTY 274 5.1.2 MOVING AVERAGE
REPRESENTATION 276 5.1.3 REPRESENTATION OF FBM ON AN INTERVAL 277 5.2
STOCHASTIC CALCULUS WITH RESPECT TO FBM 287 5.2.1 MALLIAVIN CALCULUS
WITH RESPECT TO THE FBM 287 5.2.2 STOCHASTIC CALCULUS WITH RESPECT TO
FBM. CASE H | 288 5.2.3 STOCHASTIC INTEGRATION WITH RESPECT TO FBM IN
THE CASE H 295 5.3 STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FBM
306 5.3.1 GENERALIZED STIELTJES INTEGRALS 306 5.3.2 DETERMINISTIC
DIFFERENTIAL EQUATIONS 309 5.3.3 STOCHASTIC DIFFERENTIAL EQUATIONS WITH
RESPECT TO FBM 312 5.4 VORTEX FILAMENTS BASED ON FBM 313 MALLIAVIN
CALCULUS IN FINANCE 321 6.1 BLACK-SCHOLES MODEL 321 6.1.1 ARBITRAGE
OPPORTUNITIES AND MARTINGALE MEASURES . . 323 6.1.2 COMPLETENESS AND
HEDGING 325 6.1.3 BLACK-SCHOLES FORMULA 327 6.2 INTEGRATION BY PARTS
FORMULAS AND COMPUTATION OF GREEKS . 330 6.2.1 COMPUTATION OF GREEKS FOR
EUROPEAN OPTIONS . . . . 332 6.2.2 COMPUTATION OF GREEKS FOR EXOTIC
OPTIONS 334 XIV CONTENTS 6.3 APPLICATION OF THE CLARK-OCONE FORMULA IN
HEDGING 336 6.3.1 A GENERALIZED CLARK-OCONE FORMULA 336 6.3.2
APPLICATION TO FINANCE 338 6.4 INSIDER TRADING 340 A APPENDIX 351 A.I A
GAUSSIAN FORMULA 351 A.2 MARTINGALE INEQUALITIES 351 A.3 CONTINUITY
CRITERIA 353 A.4 CARLEMAN-FREDHOLM DETERMINANT 354 A.5 FRACTIONAL
INTEGRALS AND DERIVATIVES 355 REFERENCES 357 INDEX 377
|
| adam_txt |
DAVID NUALART THE MALLIAVIN CALCULUS AND RELATED TOPICS ^J SPRINGER
CONTENTS INTRODUCTION 1 1 ANALYSIS ON THE WIENER SPACE 3 1.1 WIENER
CHAOS AND STOCHASTIC INTEGRALS 3 1.1.1 THE WIENER CHAOS DECOMPOSITION 4
1.1.2 THE WHITE NOISE CASE: MULTIPLE WIENER-ITO INTEGRALS . 8 1.1.3 ITO
STOCHASTIC CALCULUS 15 1.2 THE DERIVATIVE OPERATOR 24 1.2.1 THE
DERIVATIVE OPERATOR IN THE WHITE NOISE CASE . 31 1.3 THE DIVERGENCE
OPERATOR 36 1.3.1 PROPERTIES OF THE DIVERGENCE OPERATOR 37 1.3.2 THE
SKOROHOD INTEGRAL 40 1.3.3 THE ITO STOCHASTIC INTEGRAL AS A PARTICULAR
CASE OF THE SKOROHOD INTEGRAL 44 1.3.4 STOCHASTIC INTEGRAL
REPRESENTATION OF WIENER FUNCTIONALS 46 1.3.5 LOCAL PROPERTIES 47 1.4
THE ORNSTEIN-UHLENBECK SEMIGROUP 54 1.4.1 THE SEMIGROUP OF
ORNSTEIN-UHLENBECK 54 1.4.2 THE GENERATOR OF THE ORNSTEIN-UHLENBECK
SEMIGROUP 58 1.4.3 HYPERCONTRACTIVITY PROPERTY AND THE MULTIPLIER
THEOREM 61 1.5 SOBOLEV SPACES AND THE EQUIVALENCE OF NORMS 67 XII
CONTENTS 2 REGULARITY OF PROBABILITY LAWS 85 2.1 REGULARITY OF DENSITIES
AND RELATED TOPICS 85 2.1.1 COMPUTATION AND ESTIMATION OF PROBABILITY
DENSITIES 86 2.1.2 A CRITERION FOR ABSOLUTE CONTINUITY BASED ON THE
INTEGRATION-BY-PARTS FORMULA 90 2.1.3 ABSOLUTE CONTINUITY USING BOULEAU
AND HIRSCH'S AP- PROACH 94 2.1.4 SMOOTHNESS OF DENSITIES 99 2.1.5 .
COMPOSITION OF TEMPERED DISTRIBUTIONS WITH NONDE- GENERATE RANDOM
VECTORS 104 2.1.6 PROPERTIES OF THE SUPPORT OF THE LAW 105 2.1.7
REGULARITY OF THE LAW OF THE MAXIMUM OF CONTINUOUS PROCESSES 108 2.2
STOCHASTIC DIFFERENTIAL EQUATIONS 116 2.2.1 EXISTENCE AND UNIQUENESS OF
SOLUTIONS 117 2.2.2 WEAK DIFFERENTIABILITY OF THE SOLUTION 119 2.3
HYPOELLIPTICITY AND HORMANDER'S THEOREM 125 2.3.1 ABSOLUTE CONTINUITY IN
THE CASE OF LIPSCHITZ COEFFICIENTS 125 2.3.2 ABSOLUTE CONTINUITY UNDER
HORMANDER'S CONDITIONS . 128 2.3.3 SMOOTHNESS OF THE DENSITY UNDER
HORMANDER'S CONDITION 133 2.4 STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
142 2.4.1 STOCHASTIC INTEGRAL EQUATIONS ON THE PLANE 142 2.4.2 ABSOLUTE
CONTINUITY FOR SOLUTIONS TO THE STOCHASTIC HEAT EQUATION 151 3
ANTICIPATING STOCHASTIC CALCULUS 169 3.1 APPROXIMATION OF STOCHASTIC
INTEGRALS 169 3.1.1 STOCHASTIC INTEGRALS DEFINED BY RIEMANN SUMS .
170 3.1.2 THE APPROACH BASED ON THE L 2 DEVELOPMENT OF THE PROCESS 176
3.2 STOCHASTIC CALCULUS FOR ANTICIPATING INTEGRALS 180 3.2.1 SKOROHOD
INTEGRAL PROCESSES 180 3.2.2 CONTINUITY AND QUADRATIC VARIATION OF THE
SKOROHOD INTEGRAL 181 3.2.3 ITO'S FORMULA FOR THE SKOROHOD AND
STRATONOVICH INTEGRALS 184 3.2.4 SUBSTITUTION FORMULAS 195 3.3
ANTICIPATING STOCHASTIC DIFFERENTIAL EQUATIONS 208 3.3.1 STOCHASTIC
DIFFERENTIAL EQUATIONS IN THE SRATONOVICH SENSE 208 3.3.2 STOCHASTIC
DIFFERENTIAL EQUATIONS WITH BOUNDARY CON- DITIONS 215 CONTENTS XIII
3.3.3 STOCHASTIC DIFFERENTIAL EQUATIONS IN THE SKOROHOD SENSE 217
TRANSFORMATIONS OF THE WIENER MEASURE 225 4.1 ANTICIPATING GIRSANOV
THEOREMS 225 4.1.1 THE ADAPTED CASE 226 4.1.2 GENERAL RESULTS ON
ABSOLUTE CONTINUITY OF TRANSFORMATIONS 228 4.1.3 CONTINUOUSLY
DIFFERENTIABLE VARIABLES IN THE DIRECTION OF H 1 230 4.1.4
TRANSFORMATIONS INDUCED BY ELEMENTARY PROCESSES . . 232 4.1.5
ANTICIPATING GIRSANOV THEOREMS 234 4.2 MARKOV RANDOM FIELDS 241 4.2.1
MARKOV FIELD PROPERTY FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH
BOUNDARY CONDITIONS 242 4.2.2 MARKOV FIELD PROPERTY FOR SOLUTIONS TO
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS 249 4.2.3 CONDITIONAL
INDEPENDENCE AND FACTORIZATION PROPERTIES 258 FRACTIONAL BROWNIAN MOTION
273 5.1 DEFINITION, PROPERTIES AND CONSTRUCTION OF THE FRACTIONAL BROWN-
IAN MOTION 273 5.1.1 SEMIMARTINGALE PROPERTY 274 5.1.2 MOVING AVERAGE
REPRESENTATION 276 5.1.3 REPRESENTATION OF FBM ON AN INTERVAL 277 5.2
STOCHASTIC CALCULUS WITH RESPECT TO FBM 287 5.2.1 MALLIAVIN CALCULUS
WITH RESPECT TO THE FBM 287 5.2.2 STOCHASTIC CALCULUS WITH RESPECT TO
FBM. CASE H | 288 5.2.3 STOCHASTIC INTEGRATION WITH RESPECT TO FBM IN
THE CASE H \ 295 5.3 STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FBM
306 5.3.1 GENERALIZED STIELTJES INTEGRALS 306 5.3.2 DETERMINISTIC
DIFFERENTIAL EQUATIONS 309 5.3.3 STOCHASTIC DIFFERENTIAL EQUATIONS WITH
RESPECT TO FBM 312 5.4 VORTEX FILAMENTS BASED ON FBM 313 MALLIAVIN
CALCULUS IN FINANCE 321 6.1 BLACK-SCHOLES MODEL 321 6.1.1 ARBITRAGE
OPPORTUNITIES AND MARTINGALE MEASURES . . 323 6.1.2 COMPLETENESS AND
HEDGING 325 6.1.3 BLACK-SCHOLES FORMULA 327 6.2 INTEGRATION BY PARTS
FORMULAS AND COMPUTATION OF GREEKS . 330 6.2.1 COMPUTATION OF GREEKS FOR
EUROPEAN OPTIONS . . . . 332 6.2.2 COMPUTATION OF GREEKS FOR EXOTIC
OPTIONS 334 XIV CONTENTS 6.3 APPLICATION OF THE CLARK-OCONE FORMULA IN
HEDGING 336 6.3.1 A GENERALIZED CLARK-OCONE FORMULA 336 6.3.2
APPLICATION TO FINANCE 338 6.4 INSIDER TRADING 340 A APPENDIX 351 A.I A
GAUSSIAN FORMULA 351 A.2 MARTINGALE INEQUALITIES 351 A.3 CONTINUITY
CRITERIA 353 A.4 CARLEMAN-FREDHOLM DETERMINANT 354 A.5 FRACTIONAL
INTEGRALS AND DERIVATIVES 355 REFERENCES 357 INDEX 377 |
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| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)441320853 (DE-599)BVBBV021527185 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition |
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| id | DE-604.BV021527185 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:24:15Z |
| indexdate | 2024-07-09T20:37:51Z |
| institution | BVB |
| isbn | 9783540283287 3540283285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014743594 |
| oclc_num | 441320853 |
| open_access_boolean | |
| owner | DE-824 DE-19 DE-BY-UBM DE-M347 DE-91G DE-BY-TUM DE-739 DE-11 DE-83 DE-20 DE-188 |
| owner_facet | DE-824 DE-19 DE-BY-UBM DE-M347 DE-91G DE-BY-TUM DE-739 DE-11 DE-83 DE-20 DE-188 |
| physical | xiv, 382 Seiten |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications |
| spelling | Nualart, David 1951- Verfasser (DE-588)113130902 aut The Malliavin calculus and related topics David Nualart Second edition Berlin ; Heidelberg ; New York Springer [2006] © 2006 xiv, 382 Seiten txt rdacontent n rdamedia nc rdacarrier Probability and its applications Verjetnost - Malliavinov račun Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Malliavin-Kalkül (DE-588)4242584-0 s DE-604 Stochastische Analysis (DE-588)4132272-1 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014743594&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nualart, David 1951- The Malliavin calculus and related topics Verjetnost - Malliavinov račun Malliavin-Kalkül (DE-588)4242584-0 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4242584-0 (DE-588)4132272-1 |
| title | The Malliavin calculus and related topics |
| title_auth | The Malliavin calculus and related topics |
| title_exact_search | The Malliavin calculus and related topics |
| title_exact_search_txtP | The Malliavin calculus and related topics |
| title_full | The Malliavin calculus and related topics David Nualart |
| title_fullStr | The Malliavin calculus and related topics David Nualart |
| title_full_unstemmed | The Malliavin calculus and related topics David Nualart |
| title_short | The Malliavin calculus and related topics |
| title_sort | the malliavin calculus and related topics |
| topic | Verjetnost - Malliavinov račun Malliavin-Kalkül (DE-588)4242584-0 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Verjetnost - Malliavinov račun Malliavin-Kalkül Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014743594&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nualartdavid themalliavincalculusandrelatedtopics |