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Sharp Martingale and Semimartingale Inequalities
This monograph presents a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 1980s,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2012.
|
| Edición: | 1st ed. 2012. |
| Colección: | Monografie Matematyczne,
72 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-0348-0370-0 | ||
| 003 | DE-He213 | ||
| 005 | 20220119060514.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 120814s2012 sz | s |||| 0|eng d | ||
| 020 | |a 9783034803700 |9 978-3-0348-0370-0 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0370-0 |2 doi | |
| 050 | 4 | |a QA273.A1-274.9 | |
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| 082 | 0 | 4 | |a 519.2 |2 23 |
| 100 | 1 | |a Osękowski, Adam. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Sharp Martingale and Semimartingale Inequalities |h [electronic resource] / |c by Adam Osękowski. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a Basel : |b Springer Basel : |b Imprint: Birkhäuser, |c 2012. | |
| 300 | |a XII, 464 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Monografie Matematyczne, |x 2297-0274 ; |v 72 | |
| 505 | 0 | |a Preface.- 1. Introduction.- 2. Burkholder's method.- 3. Martingale inequalities in discrete time.- 4. Sub- and supermartingale inequalities in discrete time.- 5. Inequalities in continuous time.- 6. Inequalities for orthogonal semimartingales.- 7. Maximal inequalities.- 8. Square function inequalities -- Appendix -- Bibliography. | |
| 520 | |a This monograph presents a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 1980s, makes it possible to deduce a given inequality for semimartingales from the existence of a certain special function with some convex-type properties. Remarkably, an appropriate application of the method leads to the sharp version of the estimate under investigation, which is particularly important for applications. These include the theory of quasiregular mappings (with major implications for the geometric function theory); the boundedness of two-dimensional Hilbert transforms and a more general class of Fourier multipliers; the theory of rank-one convex and quasiconvex functions; and more. The book is divided into a number of distinct parts. In the introductory chapter we present the motivation for the results and relate them to some classical problems in harmonic analysis. The next part contains a general description of the method, which is applied in subsequent chapters to the study of sharp estimates for discrete-time martingales; discrete-time sub- and supermartingales; continuous time processes; and the square and maximal functions. Each chapter contains additional bibliographical notes included for reference purposes. | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Potential theory (Mathematics). | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Potential Theory. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783034803717 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034807494 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034803694 |
| 830 | 0 | |a Monografie Matematyczne, |x 2297-0274 ; |v 72 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-0348-0370-0 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||