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Author: Ruilin Long
Publisher: Springer Science & Business Media
ISBN: 3322992667
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This book gives a systematic introduction to the theory of martingale spaces and inequalities. Except those mainly concerned with the martingale Hp, p>1, most parts of the book reflect the developments in the field in the past twenty years. The material is self-contained, only a familiarity with basic analysis is required. Both graduate students and mathematicians who want to know about the interaction between analysis and probability will find this book to be a valuable reference and text.Das Buch gibt eine systematische Einführung in die Martingaltheorie und ihre Beziehungen zur Analysis. Der größte Teil des Buches beschreibt die Entwicklungen der letzten 20 Jahre.
Author: Ruilin Long
Publisher: Springer Science & Business Media
ISBN: 3322992667
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
This book gives a systematic introduction to the theory of martingale spaces and inequalities. Except those mainly concerned with the martingale Hp, p>1, most parts of the book reflect the developments in the field in the past twenty years. The material is self-contained, only a familiarity with basic analysis is required. Both graduate students and mathematicians who want to know about the interaction between analysis and probability will find this book to be a valuable reference and text.Das Buch gibt eine systematische Einführung in die Martingaltheorie und ihre Beziehungen zur Analysis. Der größte Teil des Buches beschreibt die Entwicklungen der letzten 20 Jahre.
Author: Ruilin Long
Publisher:
ISBN: 9787301020692
Category : Inequalities (Mathematics)
Languages : en
Pages : 344
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Book Description
Author: Adam Osękowski
Publisher: Springer Science & Business Media
ISBN: 3034803702
Category : Mathematics
Languages : en
Pages : 471
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Book Description
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.
Author: Bernard Bercu
Publisher: Springer
ISBN: 3319220993
Category : Mathematics
Languages : en
Pages : 131
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Book Description
The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.
Author: Adriano M. Garsia
Publisher:
ISBN:
Category : Inequalities (Mathematics).
Languages : en
Pages : 200
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Book Description
Author: Ferenc Weisz
Publisher: Springer
ISBN: 3540482954
Category : Mathematics
Languages : en
Pages : 228
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Book Description
This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1316679462
Category : Mathematics
Languages : en
Pages : 591
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Book Description
This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.
Author: I︠U︡riĭ Vasilʹevich Borovskikh
Publisher: VSP
ISBN: 9789067642712
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1107137241
Category : Mathematics
Languages : en
Pages : 591
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Book Description
This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Author: Masato Kikuchi
Publisher:
ISBN:
Category : Function spaces
Languages : en
Pages : 18
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Book Description
