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Sharp Martingale and semimartingale inequalities:

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Bibliographische Detailangaben
Beteilige Person:	Osękowski, Adam (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Basel Birkhäuser [2012]
Schriftenreihe:	Monografie matematyczne 72
Schlagwörter:	Martingaltheorie Martingal-Ungleichung
Links:	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
Umfang:	XI, 462 Seiten
ISBN:	9783034803694

Internformat

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Datensatz im Suchindex

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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
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indexdate	2024-12-20T16:14:14Z
institution	BVB
isbn	9783034803694
language	English
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physical	XI, 462 Seiten
publishDate	2012
publishDateSearch	2012
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publisher	Birkhäuser
record_format	marc
series	Monografie matematyczne
series2	Monografie matematyczne
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
volume_link	(DE-604)BV000003532
work_keys_str_mv	AT osekowskiadam sharpmartingaleandsemimartingaleinequalities

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