Discrete-parameter Martingales:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English French |
| Published: |
Amsterdam [u.a.]
North-Holland Published
1975
Inc ; New York American Elsevier Publishing Company |
| Series: | North-Holland mathematical library
Volume 10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 236 Seiten |
| ISBN: | 0720428106 0444107088 |
Staff View
MARC
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| 100 | 1 | |a Neveu, Jacques |d 1932-2016 |0 (DE-588)10764066X |4 aut | |
| 240 | 1 | 0 | |a Martingales à temps discret |
| 245 | 1 | 0 | |a Discrete-parameter Martingales |c J. Neveu ; translated by T. P. Speed |
| 246 | 1 | 3 | |a Discrete parameter Martingales |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland Published |c 1975 | |
| 264 | 1 | |a Inc ; New York |b American Elsevier Publishing Company | |
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| 650 | 4 | |a Martingales (Mathématiques) | |
| 650 | 4 | |a Martingales (Mathematics) | |
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| 650 | 0 | 7 | |a Martingal |0 (DE-588)4126466-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1814970684996059136 |
|---|---|
| adam_text |
TABLE OF CONTENTS
Preface v
I Preliminaries, on conditional expectations 1
1 1. Sub cr fields of a probability space 1
1 2. Conditional expectations 5
1 3. Supplement: Conditional expectations with respect to a a
finite measure 16
II Positive martingales and supermartingales 18
II l. Stopping times 19
II 2. Positive supermartingales 22 •
II 3. Exercises 33
III Applications 35
III l. Positive martingales and set functions. The Lebesgue and
Radon Nikodym theorems on the decomposition of measures 35
III 2. Applications to statistical tests 44
III 3. Haar systems and bases 51
III 4. Gaussian spaces 53
III 5. Application to Markov chains 54
IV Convergence and regularity of martingales 62
IV 1. A.s. convergence of Submartingales 62
IV 2. Regularity of integrable martingales 64
IV 3. Regular stopping times for an integrable martingale . 73
IV 4. Application: An exponential formula and Wald's identity 78
IV 5. Supplements 86
IV 5 A. Doob's inequalities 86
IV 5 B. Regularity of integrable submartingales . 91
IV 6. Exercises 93
¦vii
Viii TABLE OF CONTENTS
V Extensions of the notion of martingale 95
V l. Martingales with a directed index set 95
V 2. Vector valued martingales 100
V 3. Reversed martingales 115
VI Optimisation problems 120
VI 1. Snell's problem 120
VI 2. Application to Markov chains 130
VI 3. Applications to random walks 131
VI 4. Another application 133
VI 5. Application to sequential statistical analysis 135
VI 6. A stochastic game 137
VII Doob's decomposition of submartingales and its application
TO SQUARE INTEGRABLE MARTINGALES 145
VII 1. Generalities 145
VII 2. Asymptotic behaviour of a square integrable martingale. . 148
VII 3. Martingales with integrable pth power 157
VII 4. Gundy's condition 161
VII 5. Exercises 167
VIII Doob's decomposition of positive supermartingales . . . . 171
VIII 1. Generalities 171
VIII 2. Supplement: A remarkable duality 178
VIII 3. Quadratic variation 185
VIII 4. Martingale transforms 202
VIII 5. Exercises 206
Appendix: On the use of Young's functions in the theory of
martingales 210
A l. Young's functions 210
A 2. Orlicz spaces 213
A 3. Applications to the theory of martingales 217
References 222
Index of terminology and notation 235 |
| any_adam_object | 1 |
| author | Neveu, Jacques 1932-2016 |
| author2 | Speed, Terry 1943- |
| author2_role | trl |
| author2_variant | t s ts |
| author_GND | (DE-588)10764066X (DE-588)1089357737 |
| author_facet | Neveu, Jacques 1932-2016 Speed, Terry 1943- |
| author_role | aut |
| author_sort | Neveu, Jacques 1932-2016 |
| author_variant | j n jn |
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| ctrlnum | (OCoLC)1845653 (DE-599)BVBBV001963096 |
| 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 Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV001963096 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-06T11:02:07Z |
| institution | BVB |
| isbn | 0720428106 0444107088 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001280238 |
| oclc_num | 1845653 |
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| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 DE-12 |
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| physical | viii, 236 Seiten |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | North-Holland Published American Elsevier Publishing Company |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Neveu, Jacques 1932-2016 (DE-588)10764066X aut Martingales à temps discret Discrete-parameter Martingales J. Neveu ; translated by T. P. Speed Discrete parameter Martingales Amsterdam [u.a.] North-Holland Published 1975 Inc ; New York American Elsevier Publishing Company viii, 236 Seiten txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library Volume 10 Martingales (Mathématiques) Martingales (Mathematics) Stochastik (DE-588)4121729-9 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Martingal (DE-588)4126466-6 s DE-604 Stochastik (DE-588)4121729-9 s Speed, Terry 1943- (DE-588)1089357737 trl Erscheint auch als Online-Ausgabe 978-0-7204-2810-0 North-Holland mathematical library Volume 10 (DE-604)BV000005206 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neveu, Jacques 1932-2016 Discrete-parameter Martingales North-Holland mathematical library Martingales (Mathématiques) Martingales (Mathematics) Stochastik (DE-588)4121729-9 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4126466-6 |
| title | Discrete-parameter Martingales |
| title_alt | Martingales à temps discret Discrete parameter Martingales |
| title_auth | Discrete-parameter Martingales |
| title_exact_search | Discrete-parameter Martingales |
| title_full | Discrete-parameter Martingales J. Neveu ; translated by T. P. Speed |
| title_fullStr | Discrete-parameter Martingales J. Neveu ; translated by T. P. Speed |
| title_full_unstemmed | Discrete-parameter Martingales J. Neveu ; translated by T. P. Speed |
| title_short | Discrete-parameter Martingales |
| title_sort | discrete parameter martingales |
| topic | Martingales (Mathématiques) Martingales (Mathematics) Stochastik (DE-588)4121729-9 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Martingales (Mathématiques) Martingales (Mathematics) Stochastik Martingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005206 |
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