Semimartingales and their stochastic calculus on manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | French English |
| Published: |
Montreal
Presses de l'Univ. de Montreal
1984
|
| Series: | Collection de la Chaire Aisenstadt
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 187 S. graph. Darst. |
| ISBN: | 2760606600 |
Staff View
MARC
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| 245 | 1 | 0 | |a Semimartingales and their stochastic calculus on manifolds |
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| 300 | |a 187 S. |b graph. Darst. | ||
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| 490 | 0 | |a Collection de la Chaire Aisenstadt | |
| 650 | 4 | |a Intégrales stochastiques | |
| 650 | 4 | |a Martingales (Mathématiques) | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Semimartingales (Mathematics) | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Semimartingal |0 (DE-588)4180967-1 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804117841937432576 |
|---|---|
| adam_text | TABLE OF CONTENTS
AVANT PROPOS 7
TABLE DES MATIERES 11
INTRODUCTION 13
INTRODUCTION 17
CHAPTER 1 : BACKGROUND FROM THE GENERAL THEORY
OF PROCESSES 21
1. Processes and stopping times 21
2. Martingales and local martingales 25
3. Semimartingales 31
4. Optional and predictable a algebras 33
5. Quasimartingales and oblique brackets 39
CHAPTER 2 : REAL STOCHASTIC INTEGRATION 47
1. Orientation 47
2. Outline of construction 53
3. Inverse problem; consequences 59
4. The optional integral 63
CHAPTER 3 : SEMIMARTINGALE TOPOLOGIES;
SQUARE BRACKETS 67
CHAPTER 4 : INTEGRABILITY; FORMAL MEASURES
AND FORMAL SEMIMARTINGALES 75
1. Integrability 75
2. Formal measures 83
3. Formal semimartingales 86
10 Table of oont nts
CHAPTER 5 : THEOREMS OF EQUIVALENCE 91
CHAPTER 6 : ITO S FORMULA 99
CHAPTER 7 : SEMIMARTINGALES WITH VALUES IN A MANIFOLD 105
1. Introduction 105
2. Localization principle; applications 109
3. Appendix: integration with respect
to a locally defined semimartingale 119
CHAPTER 8 : STOCHASTIC INTEGRATION ON A MANIFOLD 123
1. Orientation 123
2. Second order differential geometry:
T!(M) and T2(M) 126
3. Second order differential geometry:
T*1(M) and T*2(M) 133
4. Transformations 136
5. Integration along a continuous
semimartingale 138
6. Appendix 150
CHAPTER 9 : THE TANGENT SPACE TO A SEMIMARTINGALE
AND TANGENTIAL REPRESENTATIONS 153
CHAPTER 10: STOCHASTIC DIFFERENTIAL EQUATIONS 159
CHAPTER 11: LIFTING OF A SEMIMARTINGALE
KITH RESPECT TO A CONNECTION 173
REFERENCES 181
INDEX OF DEFINED TERMS (IN ALPHABETICAL ORDER) 183
INDEX OF SYMBOLS (IN ORDER OF FIRST OCCURRENCE) 186
TABLE DES MATIERES
AVANT PROPOS 7
TABLE OF CONTENTS 0
INTRODUCTION 13
INTRODUCTION 17
CHAPITRE 1 : RAPPELS DE THEORIE GENERALE
DES PROCESSUS 21
1. Processus et temps d arrêt 21
2. Martingales et martingales locales 25
3. Semi martingales 31
4. Tribus optionnelle et prévisible 33
5. Quasi martingales et crochets
obliques 39
CHAPITRE 2 : INTEGRATION STOCHASTIQUE REELLE 47
1. Orientation 47
2. Grandes lignes de la construction 53
3. Problème inverse; conséquences 59
4. L intégrale optionnelle 63
CHAPITRE 3 : TOPOLOGIE DES SEMI MARTINGALES;
CROCHETS DROITS 67
CHAPITRE 4 : INTEGRABILITE; MESURES FORMELLES
ET SEMI MARTINGALES FORMELLES 75
1. Intégràbilité 75
2. Mesures formelles 83
12 Table des matières
5. Semi martingales formelles 86
CHAPITRE 5 : THEOREMES D EQUIVALENCE 91
CHAtliRE 6 : FORMULE D ITO 99
CHAPITRE ? : SEMI MARTINGALES A VALEURS
DANS UNE VARIETE 105
1. Introduction 105
2. Principe de localisation;
applications 109
3. Appendice: intégration par
rapport à des semi martingales
définies localement 119
CHAPITRE 8 : INTEGRATION STOCHASTIQUE SUR UNE VARIETE 123
1. Orientation 123
2. Géométrie différentielle du
second ordre: Tl(M) et T2(M) 126
S. Géométrie différentielle du
second ordre: T*l(M) et T*2(M) 133
4. Transformations 136
5. Intégration le long d une
semi martingale continue 138
6. Appendice 150
CHAPITRE 9: L ESPACE TANGENT A UNE SEMIMARTINGALE
ET REPRESENTATIONS TANGENT TELLES 153
CHAPITRE 10: EQUATIONS DIFFERENTIELLES STOCHASTIQUES 159
CHAPITRE 11: RELEVEMENT D UNE SEMI hiART IN GALE
PAR UNE CONNEXION 173
REFERENCES 181
INDEX DES TERMES DEFINIS (DANS L ORDRE ALPHABETIQUE) 183
INDEX DES SYMBOLES (DANS L ORDRE DE PREMIERE APPARITION) 186
|
| any_adam_object | 1 |
| author | Schwartz, Laurent 1915-2002 |
| author_GND | (DE-588)118795694 |
| author_facet | Schwartz, Laurent 1915-2002 |
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| ctrlnum | (OCoLC)12407915 (DE-599)BVBBV003495833 |
| dewey-full | 519.2/87 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/87 |
| dewey-search | 519.2/87 |
| dewey-sort | 3519.2 287 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003495833 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:00:49Z |
| institution | BVB |
| isbn | 2760606600 |
| language | French English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002215772 |
| oclc_num | 12407915 |
| open_access_boolean | |
| owner | DE-384 DE-11 DE-188 |
| owner_facet | DE-384 DE-11 DE-188 |
| physical | 187 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Presses de l'Univ. de Montreal |
| record_format | marc |
| series2 | Collection de la Chaire Aisenstadt |
| spelling | Schwartz, Laurent 1915-2002 Verfasser (DE-588)118795694 aut Semimartingales and their stochastic calculus on manifolds Montreal Presses de l'Univ. de Montreal 1984 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Collection de la Chaire Aisenstadt Intégrales stochastiques Martingales (Mathématiques) Variétés (Mathématiques) Manifolds (Mathematics) Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd rswk-swf Semimartingal (DE-588)4180967-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002215772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwartz, Laurent 1915-2002 Semimartingales and their stochastic calculus on manifolds Intégrales stochastiques Martingales (Mathématiques) Variétés (Mathématiques) Manifolds (Mathematics) Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd |
| subject_GND | (DE-588)4180967-1 |
| title | Semimartingales and their stochastic calculus on manifolds |
| title_auth | Semimartingales and their stochastic calculus on manifolds |
| title_exact_search | Semimartingales and their stochastic calculus on manifolds |
| title_full | Semimartingales and their stochastic calculus on manifolds |
| title_fullStr | Semimartingales and their stochastic calculus on manifolds |
| title_full_unstemmed | Semimartingales and their stochastic calculus on manifolds |
| title_short | Semimartingales and their stochastic calculus on manifolds |
| title_sort | semimartingales and their stochastic calculus on manifolds |
| topic | Intégrales stochastiques Martingales (Mathématiques) Variétés (Mathématiques) Manifolds (Mathematics) Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd |
| topic_facet | Intégrales stochastiques Martingales (Mathématiques) Variétés (Mathématiques) Manifolds (Mathematics) Semimartingales (Mathematics) Stochastic processes Semimartingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002215772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schwartzlaurent semimartingalesandtheirstochasticcalculusonmanifolds |