Inequalities In Analysis And Probability Third Edition
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Inequalities In Analysis And Probability Third Edition
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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2021-10-18
Inequalities In Analysis And Probability Third Edition written by Odile Pons and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-18 with Mathematics categories.
The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.
Concentration Of Measure Inequalities In Information Theory Communications And Coding
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Author : Maxim Raginsky
language : en
Publisher:
Release Date : 2014
Concentration Of Measure Inequalities In Information Theory Communications And Coding written by Maxim Raginsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Computers categories.
Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.
Probability Inequalities
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Author : Zhengyan Lin
language : en
Publisher: Springer
Release Date : 2014-12-09
Probability Inequalities written by Zhengyan Lin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-09 with Mathematics categories.
Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.
Analysis And Differential Equations Second Edition
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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2022-12-19
Analysis And Differential Equations Second Edition written by Odile Pons and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-19 with Mathematics categories.
The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.
Probability Inequalities In Multivariate Distributions
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Author : Yung Liang Tong
language : en
Publisher:
Release Date : 1980
Probability Inequalities In Multivariate Distributions written by Yung Liang Tong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Inequalities for multivariate normal distribution; Inequalities for other well-known distributions; Integral inequalities over a symmetric convex set; Inequalities via dependence association and mixture; Inequalities via majorization and weak majorization; Distribution-free inequalities; Some applications.
The Collected Works Of Wassily Hoeffding
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Author : Wassily Hoeffding
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Collected Works Of Wassily Hoeffding written by Wassily Hoeffding 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 2012-12-06 with Mathematics categories.
It has been a rare privilege to assemble this volume of Wassily Hoeffding's Collected Works. Wassily was, variously, a teacher, supervisor and colleague to us, and his work has had a profound influence on our own. Yet this would not be sufficient reason to publish his collected works. The additional and overwhelmingly compelling justification comes from the fun damental nature of his contributions to Statistics and Probability. Not only were his ideas original, and far-reaching in their implications; Wassily de veloped them so completely and elegantly in his papers that they are still cited as prime references up to half a century later. However, three of his earliest papers are cited rarely, if ever. These include material from his doctoral dissertation. They were written in German, and two of them were published in relatively obscure series. Rather than reprint the original articles, we have chosen to have them translated into English. These trans lations appear in this book, making Wassily's earliest research available to a wide audience for the first time. All other articles (including those of his contributions to Mathematical Reviews which go beyond a simple reporting of contents of articles) have been reproduced as they appeared, together with annotations and corrections made by Wassily on some private copies of his papers. Preceding these articles are three review papers which dis cuss the . impact of his work in some of the areas where he made major contributions.
Concentration Inequalities For Sums And Martingales
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Author : Bernard Bercu
language : en
Publisher: Springer
Release Date : 2015-09-29
Concentration Inequalities For Sums And Martingales written by Bernard Bercu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
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.
Analysis And Probability
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Author : Aurel Spataru
language : en
Publisher: Newnes
Release Date : 2013-01-12
Analysis And Probability written by Aurel Spataru and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-12 with Mathematics categories.
Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology and fundamental results of probability theory. Exercises are included throughout the text, not just at the end, to teach each concept fully as it is explained, including presentations of interesting extensions of the theory. The complete and detailed nature of the book makes it ideal as a reference book or for self-study in probability and related fields. - Covers a wide range of subjects including f-expansions, Fuk-Nagaev inequalities and Markov triples. - Provides multiple clearly worked exercises with complete proofs. - Guides readers through examples so they can understand and write research papers independently.
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 >.
Probability And Measure
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Author : Patrick Billingsley
language : en
Publisher: John Wiley & Sons
Release Date : 2017
Probability And Measure written by Patrick Billingsley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes