Some Sharp Inequalities For Martingale Transforms

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Some Sharp Inequalities For Martingale Transforms

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Author : Kwok Pui Choi
language : en
Publisher:
Release Date : 1987

Some Sharp Inequalities For Martingale Transforms written by Kwok Pui Choi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

Sharp Martingale And Semimartingale Inequalities

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Author : Adam Osękowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-14

Sharp Martingale And Semimartingale Inequalities written by Adam Osękowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-14 with Mathematics categories.

This monograph is a presentation of 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 80s, enables 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 deep implications to the geometric function theory); the boundedness of two-dimensional Hilbert transform 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 few separate parts. In the introductory chapter we present 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; the square and maximal functions. Each chapter contains additional bibliographical notes included for reference.​

Martingale Inequalities Seminar Notes On Recent Progress

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Author : Adriano M. Garsia
language : en
Publisher:
Release Date : 1973

Martingale Inequalities Seminar Notes On Recent Progress written by Adriano M. Garsia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Inequalities (Mathematics). categories.

Selected Works Of Donald L Burkholder

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Author : Burgess Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-18

Selected Works Of Donald L Burkholder written by Burgess Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-18 with Mathematics categories.

This book chronicles Donald Burkholder's thirty-five year study of martingales and its consequences. Here are some of the highlights. Pioneering work by Burkholder and Donald Austin on the discrete time martingale square function led to Burkholder and Richard Gundy's proof of inequalities comparing the quadratic variations and maximal functions of continuous martingales, inequalities which are now indispensable tools for stochastic analysis. Part of their proof showed how novel distributional inequalities between the maximal function and quadratic variation lead to inequalities for certain integrals of functions of these operators. The argument used in their proof applies widely and is now called the Burkholder-Gundy good lambda method. This uncomplicated and yet extremely elegant technique, which does not involve randomness, has become important in many parts of mathematics. The continuous martingale inequalities were then used by Burkholder, Gundy, and Silverstein to prove the converse of an old and celebrated theorem of Hardy and Littlewood. This paper transformed the theory of Hardy spaces of analytic functions in the unit disc and extended and completed classical results of Marcinkiewicz concerning norms of conjugate functions and Hilbert transforms. While some connections between probability and analytic and harmonic functions had previously been known, this single paper persuaded many analysts to learn probability. These papers together with Burkholder's study of martingale transforms led to major advances in Banach spaces. A simple geometric condition given by Burkholder was shown by Burkholder, Terry McConnell, and Jean Bourgain to characterize those Banach spaces for which the analog of the Hilbert transform retains important properties of the classical Hilbert transform. Techniques involved in Burkholder's usually successful pursuit of best constants in martingale inequalities have become central to extensive recent research into two well- known open problems, one involving the two dimensional Hilbert transform and its connection to quasiconformal mappings and the other a conjecture in the calculus of variations concerning rank-one convex and quasiconvex functions. This book includes reprints of many of Burkholder's papers, together with two commentaries on his work and its continuing impact.

Inequalities And Extremal Problems In Probability And Statistics

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Author : Iosif Pinelis
language : en
Publisher: Academic Press
Release Date : 2017-05-10

Inequalities And Extremal Problems In Probability And Statistics written by Iosif Pinelis and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-10 with Mathematics categories.

Inequalities and Extremal Problems in Probability and Statistics: Selected Topics presents various kinds of useful inequalities that are applicable in many areas of mathematics, the sciences, and engineering. The book enables the reader to grasp the importance of inequalities and how they relate to probability and statistics. This will be an extremely useful book for researchers and graduate students in probability, statistics, and econometrics, as well as specialists working across sciences, engineering, financial mathematics, insurance, and mathematical modeling of large risks. Teaches users how to understand useful inequalities Applicable across mathematics, sciences, and engineering Presented by a team of leading experts

Harmonic Mappings And Minimal Immersion

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Author : Enrico Giusti
language : en
Publisher: Springer
Release Date : 2006-11-14

Harmonic Mappings And Minimal Immersion written by Enrico Giusti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Schr Dinger Operators Como 1984

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Author : Sandro Graffi
language : en
Publisher: Springer
Release Date : 2006-11-14

Schr Dinger Operators Como 1984 written by Sandro Graffi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.

Handbook Of The Geometry Of Banach Spaces

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Author :
language : en
Publisher: Elsevier
Release Date : 2001-08-15

Handbook Of The Geometry Of Banach Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-15 with Mathematics categories.

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Harmonic Analysis And Partial Differential Equations

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Author : Jose Garcia-Cuerva
language : en
Publisher: Springer
Release Date : 2006-11-14

Harmonic Analysis And Partial Differential Equations written by Jose Garcia-Cuerva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The programme of the Conference at El Escorial included 4 main courses of 3-4 hours. Their content is reflected in the four survey papers in this volume (see above). Also included are the ten 45-minute lectures of a more specialized nature.

New Trends In Applied Harmonic Analysis Volume 2

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Author : Akram Aldroubi
language : en
Publisher: Springer Nature
Release Date : 2019-11-26

New Trends In Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.