Martingale Spaces And Inequalities
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Martingale Spaces And Inequalities
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Author : Ruilin Long
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Martingale Spaces And Inequalities written by Ruilin Long 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 2013-11-11 with Mathematics categories.
In the past twenty years, the Hp-BMO Theory on Rn has undergone a flourishing development, which should partly give the credit to the application of some martin gale idea and methods. It would be valuable to exhibit some examples concerning this point. As one of the key parts of Calder6n-Zygmund's real method which first appeared in the 50's, Calder6n-Zygmund Decomposition is exactly the so-called stopping time argument in nature which already existed in the Probability Theory early in the 30's, although such a close relationship between Calder6n-Zygmund De composition and the stopping time argument perhaps was not realized consciously at that time. But after the 70's we actually used the stopping time argument in tentionally as a method of thinking in Analysis. Later, when classical Hp Theory had undergone an evolution from one chapter in the Complex Variable Theory to an independent branch (the key step to accelerate this evolution was D. Burkholder R. Gundy-M. Silverstein's well-known work in the early 70's on the maximal function characterization of Hp), Martingale Hp-BMO Theory soon appeared as a counter part of the classical Hp-BMO Theory. Owing to the simplicity of the structure in martingale setting, many new ideas and methods might be produced easier on this stage. These new things have shown a great effect on the classical Hp-BMO The ory. For example, the concept of atomic decomposition of H P was first germinated in martingale setting; the good >.
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 Spaces And Inequalities
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Author : Ruilin Long
language : en
Publisher:
Release Date : 1993
Martingale Spaces And Inequalities written by Ruilin Long and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Inequalities (Mathematics) categories.
Martingales In Banach Spaces
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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-06
Martingales In Banach Spaces written by Gilles Pisier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Classical Potential Theory And Its Probabilistic Counterpart
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Author : Joseph L. Doob
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-12
Classical Potential Theory And Its Probabilistic Counterpart written by Joseph L. Doob 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 2001-01-12 with Mathematics categories.
From the reviews: "Here is a momumental work by Doob, one of the masters, in which Part 1 develops the potential theory associated with Laplace's equation and the heat equation, and Part 2 develops those parts (martingales and Brownian motion) of stochastic process theory which are closely related to Part 1". --G.E.H. Reuter in Short Book Reviews (1985)
Probability With Martingales
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Author : David Williams
language : en
Publisher: Cambridge University Press
Release Date : 1991-02-14
Probability With Martingales written by David Williams and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-14 with Mathematics categories.
This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.
Martingale Limit Theory And Its Application
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Author : P. Hall
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Martingale Limit Theory And Its Application written by P. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Measures Integrals And Martingales
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Author : René L. Schilling
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-10
Measures Integrals And Martingales written by René L. Schilling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Mathematics categories.
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached at http: //www.motapa.de/measures_integrals_and_martingales/index.htm
Operator Theory And Harmonic Analysis
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Author : Alexey N. Karapetyants
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Operator Theory And Harmonic Analysis written by Alexey N. Karapetyants and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Mixed Norm Inequalities And Operator Space L P Embedding Theory
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Author : Marius Junge
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Mixed Norm Inequalities And Operator Space L P Embedding Theory written by Marius Junge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.