Semimartingales: a course on stochastic processes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
de Gruyter
1982
|
| Series: | De Gruyter studies in mathematics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 287 Seiten |
| ISBN: | 3110086743 9783110086744 |
Staff View
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| 100 | 1 | |a Métivier, Michel |d 1931-1988 |0 (DE-588)172256585 |4 aut | |
| 245 | 1 | 0 | |a Semimartingales |b a course on stochastic processes |c Michel Métivier |
| 264 | 1 | |a Berlin ; New York |b de Gruyter |c 1982 | |
| 300 | |a XI, 287 Seiten | ||
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| 490 | 1 | |a De Gruyter studies in mathematics |v 2 | |
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| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Semimartingales (Mathematics) | |
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Record in the Search Index
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Contents
Part I: Martingales Quasi martingales Semimartingales
Chapter 1: Basic notions on stochastic processes
1. Stochastic basic Stochastic processes 3
2. Examples and construction of stochastic processes 5
3. Well measurable (or optional) and predictable processes 9
4. Stopping times 11
5. The a algebras J^ and J*v 17
6. Admissible measures 22
7. Decomposition theorems for stopping times 28
Exercise and supplements 32
Historical and bibliographical notes 38
Chapter 2: Martingales and quasimartingales Basic inequalities and convergence
theorem Application to stochastic algorithms
8. Martingales, submartingales, supermartingales, quasimartingales:
elementary properties 40
9. Doob's inequalities for real quasimartingales and the almost sure
convergence theorem 46
10. Uniform integrability Convergence in LP Regularity properties of
trajectories 53
11. Convergence theorems for vector valued quasimartingales 60
12. A typical application of quasimartingale convergence theorems:
convergence of stochastic algorithms 66
Exercises and supplements 72
Historical and bibliographical notes 79
Chapter 3: Quasimartingales form class \L. D]
Predictable and dual predictable projection of processes
13. Doleans measure of an [L. £ ] quasimartingale 80
14. Predictable projection of a process and dual predictable projection of an
admissible measure 88
X Contents
15. The predictable F. V. process of an admissible measure on A and the
Doob Meyer decomposition of a quasimartingale 94
Exercises and supplements 102
Historical and bibliographical notes 110
Chapter 4: Square integrable Martingales and semimartingales
16. Spaces of real L2 martingales 112
17. The first increasing process and orthogonality of L2 martingales 115
18. TheL2 stochastic integral and the quadratic variation of an L2 martingale . 120
19. Stopped martingales. Inequalities 128
20. Spaces of Hibert valued martingales 132
21. The process 4M of a square integrable Hilbert valued martingale 136
22. The isometric stochastic integral with respect to Hilbert valued martingales 142
23. Localisation of processes and semimartingales 148
Exercises and supplements 158
Historical and bibliographical notes 163
Part II: Stochastic Calculus
Chapter 5: Stochastic integral with respect to semimartingales and the
transformation formula
24. Stochastic integral in the real case 168
25. Quadratic variation and the transformation theorem 175
26. Stochastic integral with respect to multidimensional semimartingales and
tensor quadratic variation 182
27. The transformation formula in the multidimensional case 188
Exercises and supplements 191
Historical and bibliographical notes 196
Chapter 6: First applications of the transformation theorem
28. Characterizations of Brownian and Poisson processes 198
29. Exponential formulas and linear stochastic differential equations 202
30. Absolutely continuous changes of probablity 207
Exercises and supplements 212
Historical and bibliographical notes 215
Chapter 7: Random measures and local characteristics of a semimartingale
31. Stochastic integral with respect to a white random measures 217
32. Local characteristics of a semimartingale Diffusions Martingale problems. 231
Contents XI
Exercises and supplements 235
Historical and bibliographical notes 238
Chapter 8: Stochastic differential equations
33. Examples of stochastic equations Definitions 240
34. Strong solutions under Lipschitz hypotheses 243
35. Conditions for non explosion 252
36. Pathwise regularity of solutions of equations depending on a parameter . 255
37. Weak solutions of some stochastic differential equations 262
Exercises and supplements 267
Historical and bibliographical notes 271
Bibliography 273
Index of notation 284
Index 286 |
| any_adam_object | 1 |
| author | Métivier, Michel 1931-1988 |
| author_GND | (DE-588)172256585 |
| author_facet | Métivier, Michel 1931-1988 |
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| classification_rvk | SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)8806621 (DE-599)BVBBV001791381 |
| 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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| illustrated | Not Illustrated |
| indexdate | 2025-01-21T17:00:45Z |
| institution | BVB |
| isbn | 3110086743 9783110086744 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001207159 |
| oclc_num | 8806621 |
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| physical | XI, 287 Seiten |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Métivier, Michel 1931-1988 (DE-588)172256585 aut Semimartingales a course on stochastic processes Michel Métivier Berlin ; New York de Gruyter 1982 XI, 287 Seiten txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 2 Martingales (Mathématiques) Processus stochastiques Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Semimartingal (DE-588)4180967-1 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Martingal (DE-588)4126466-6 s Erscheint auch als Online-Ausgabe 978-3-11-084556-3 De Gruyter studies in mathematics 2 (DE-604)BV000005407 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001207159&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Métivier, Michel 1931-1988 Semimartingales a course on stochastic processes De Gruyter studies in mathematics Martingales (Mathématiques) Processus stochastiques Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4180967-1 (DE-588)4126466-6 (DE-588)4057630-9 |
| title | Semimartingales a course on stochastic processes |
| title_auth | Semimartingales a course on stochastic processes |
| title_exact_search | Semimartingales a course on stochastic processes |
| title_full | Semimartingales a course on stochastic processes Michel Métivier |
| title_fullStr | Semimartingales a course on stochastic processes Michel Métivier |
| title_full_unstemmed | Semimartingales a course on stochastic processes Michel Métivier |
| title_short | Semimartingales |
| title_sort | semimartingales a course on stochastic processes |
| title_sub | a course on stochastic processes |
| topic | Martingales (Mathématiques) Processus stochastiques Semimartingales (Mathematics) Stochastic processes Semimartingal (DE-588)4180967-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Martingales (Mathématiques) Processus stochastiques Semimartingales (Mathematics) Stochastic processes Semimartingal Martingal Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001207159&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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