Sharp Martingale and semimartingale inequalities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel
Birkhäuser
[2012]
|
| Series: | Monografie matematyczne
72 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 462 Seiten |
| ISBN: | 9783034803694 |
Staff View
MARC
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| 245 | 1 | 0 | |a Sharp Martingale and semimartingale inequalities |c by Adam Osękowski |
| 264 | 1 | |a Basel |b Birkhäuser |c [2012] | |
| 264 | 4 | |c © 2012 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
...................................... xi
1
Introduction
................................. 1
2
Burkholder s
Method
2.1
Description
of the
technique
..................... 9
2.2
Further remarks
............................ 18
2.3
Integration method
.......................... 21
2.4
Notes and comments
......................... 22
3
Martingale Inequalities in Discrete Time
3.1
Weak type estimates, general case
.................. 23
3.2
Weak type estimates for
nonnegative
ƒ............... 50
3.3
Lp estimates
.............................. 53
3.4
Estimates for moments of different order
.............. 59
3.5
Nonnegative
martingales
....................... 67
3.6
Logarithmic estimates
........................ 71
3.7
Inequalities for bounded martingales
................ 78
3.8
Inequalities for nonsymmetric martingale transforms
....... 88
3.9
On optimal control of martingales
.................. 97
3.10
Inequalities for weakly dominated martingales
...........
Ill
3.11
UMD spaces
.............................. 120
3.12
Escape inequalities
.......................... 130
3.13
The dyadic case and inequalities for the
Haar
system
....... 136
3.14
Notes and comments
......................... 138
4
Sub- and
Supermartingale
Inequalities in Discrete Time
4.1
α
-strong differential subordination and
α
-subordination.....
143
4.2
Weak type estimates for general sub- or
supermartingales
.... 146
4.3
Weak type inequalities for
nonnegative sub-
and
supermartingales
........................... 154
4.4
Moment estimates for
submartingales
................ 160
4.5
Moment
estimates for
supermartingales
.............. 167
4.6
Logarithmic estimates
........................ 170
4.7
Inequalities for bounded sub- and
supermartingales
........ 183
4.8
On the optimal control of
nonnegative
submartingales......
199
4.9
Escape inequalities
.......................... 208
4.10
Notes and comments
......................... 209
Inequalities in Continuous Time
5.1
Dominations in the continuous-time case
.............. 211
5.2
Inequalities for stochastic integrals and Bichteler s theorem
. . . 214
5.3
Burkholder s method in continuous time
.............. 216
5.4
Inequalities for continuous-time martingales
............ 227
5.5
Inequalities for continuous-time sub- and
supermartingales
.... 236
5.6
Inequalities for smooth functions on Euclidean domains
..... 241
5.7
Notes and comments
......................... 243
Inequalities for Orthogonal Semimartingales
6.1
Orthogonality and modification of Burkholder s method
..... 245
6.2
Weak type inequalities for martingales
............... 247
6.3
Lp inequalities for local martingales
................. 252
6.4
Inequalities for moments of different order
............. 267
6.5
Logarithmic estimates
........................ 272
6.6
Moment inequalities for
nonnegative
martingales
......... 273
6.7
Weak type inequalities for
submartingales
............. 275
6.8
Moment inequalities for
submartingales
.............. 281
6.9
Inequalities for orthogonal smooth functions
............ 284
6.10
Lp estimates for
conformai
martingales and Bessel processes
. . . 285
6.11
Notes and comments
......................... 292
Maximal Inequalities
7.1
Modification of Burkholder s method
................ 295
7.2
Doob-type inequalities
........................ 300
7.3
Maximal L1 estimates for martingales
............... 308
7.4
Maximal Lp inequalities
....................... 323
7.5
Double maximal inequality
...................... 334
7.6
Double maximal inequality for
nonnegative
martingales
..... 346
7.7
Bounds for one-sided maximal functions
.............. 347
7.8
Lp bounds for one-sided maximal function
............. 358
7.9
Burkholder s method for continuous-path semimartingales
.... 368
7.10
Maximal bounds for continuous-path martingales
......... 372
7.11
A maximal bound for continuous-path
supermartingales
..... 381
7.12
A maximal bound for continuous-path
submartingales
...... 386
7.13
Notes
and comments
......................... 392
8
Square Function Inequalities
8.1
Modification of Burkholder s method
................ 393
8.2
Weak type estimates
......................... 396
8.3
Moment estimates
.......................... 413
8.4
Moment estimates for
nonnegative
martingales
.......... 420
8.5
Ratio inequalities
........................... 423
8.6
Maximal inequalities
......................... 427
8.7
Inequalities for the conditional square function
.......... 435
8.8
Notes and comments
......................... 444
Appendix
A.I Confluent hypergeometric functions and their properties
..... 447
A.
2
Parabolic cylinder functions and their properties
......... 447
Bibliography
................................... 451
|
| any_adam_object | 1 |
| author | Osękowski, Adam |
| author_GND | (DE-588)1029109389 |
| author_facet | Osękowski, Adam |
| author_role | aut |
| author_sort | Osękowski, Adam |
| author_variant | a o ao |
| building | Verbundindex |
| bvnumber | BV040401138 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)811610253 (DE-599)BVBBV040401138 |
| dewey-full | 519.236 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.236 |
| dewey-search | 519.236 |
| dewey-sort | 3519.236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040401138 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:23:13Z |
| institution | BVB |
| isbn | 9783034803694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025254331 |
| oclc_num | 811610253 |
| open_access_boolean | |
| owner | DE-739 DE-384 DE-11 DE-83 |
| owner_facet | DE-739 DE-384 DE-11 DE-83 |
| physical | XI, 462 Seiten |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monografie matematyczne |
| series2 | Monografie matematyczne |
| spelling | Osękowski, Adam (DE-588)1029109389 aut Sharp Martingale and semimartingale inequalities by Adam Osękowski Basel Birkhäuser [2012] © 2012 XI, 462 Seiten txt rdacontent n rdamedia nc rdacarrier Monografie matematyczne 72 Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Martingal-Ungleichung (DE-588)4168983-5 gnd rswk-swf Martingaltheorie (DE-588)4168982-3 s Martingal-Ungleichung (DE-588)4168983-5 s DE-604 Monografie matematyczne 72 (DE-604)BV000003532 72 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025254331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Osękowski, Adam Sharp Martingale and semimartingale inequalities Monografie matematyczne Martingaltheorie (DE-588)4168982-3 gnd Martingal-Ungleichung (DE-588)4168983-5 gnd |
| subject_GND | (DE-588)4168982-3 (DE-588)4168983-5 |
| title | Sharp Martingale and semimartingale inequalities |
| title_auth | Sharp Martingale and semimartingale inequalities |
| title_exact_search | Sharp Martingale and semimartingale inequalities |
| title_full | Sharp Martingale and semimartingale inequalities by Adam Osękowski |
| title_fullStr | Sharp Martingale and semimartingale inequalities by Adam Osękowski |
| title_full_unstemmed | Sharp Martingale and semimartingale inequalities by Adam Osękowski |
| title_short | Sharp Martingale and semimartingale inequalities |
| title_sort | sharp martingale and semimartingale inequalities |
| topic | Martingaltheorie (DE-588)4168982-3 gnd Martingal-Ungleichung (DE-588)4168983-5 gnd |
| topic_facet | Martingaltheorie Martingal-Ungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025254331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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