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Inequalities In Analysis And Probability

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Inequalities In Analysis And Probability

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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2016-11-03

Inequalities In Analysis And Probability 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 2016-11-03 with Mathematics categories.

The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

Inequalities In Analysis And Probability

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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2012-11-29

Inequalities In Analysis And Probability

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Author : Odile Pons
language : en
Publisher: World Scientific
Release Date : 2013

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.

Some Topics In Probability And Analysis

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Author : R. F. Gundy
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Some Topics In Probability And Analysis written by R. F. Gundy 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 1989 with Mathematics categories.

This book is based on lectures presented by the author at DePaul University in July 1986. The lectures cover three main topics. The first is local time theory for Brownian motion and some geometrical inequalities for harmonic functions in the upper half-plane $R^{n+1}_+$. The author sketches a proof of the inequalities obtained by Barlow and Yor for the maximal local time functional. The second topic concerns a probabilistic treatment of Riesz transforms in $R^{n+1}_+$, and semimartingale inequalities. The author proves semimartingale inequalities of the type usually obtained for martingales. The final topic centers on a discussion of the Ornstein-Uhlenbeck semigroup and P. A. Meyer's extension of the Riesz inequalities for the infinite-dimensional version of this semigroup. One of the major results of the book is the establishment of inequalities for the density of the area integral.

Probabilistic Inequalities

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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2009-08-11

Probabilistic Inequalities written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-11 with Mathematics categories.

In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end.The topics covered in this unique book are wide-ranging and diverse. The opening chapters examine the probabilistic Ostrowski type inequalities, and various related ones, as well as the largely discusses about the Grothendieck type probabilistic inequalities. The book is also about inequalities in information theory and the Csiszar's f-Divergence between probability measures. A great section of the book is also devoted to the applications in various directions of Geometry Moment Theory. Also, the development of the Grüss type and Chebyshev-Grüss type inequalities for Stieltjes integrals and the applications in probability are explored in detail. The final chapters discuss the important real analysis methods with potential applications to stochastics. The book will be of interest to researchers and graduate students, and it is also seen as an invaluable reference book to be acquired by all science libraries as well as seminars that conduct discussions on related topics.

Advances In Inequalities From Probability Theory And Statistics

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Author : Neil S. Barnett
language : en
Publisher: Nova Publishers
Release Date : 2008

Advances In Inequalities From Probability Theory And Statistics written by Neil S. Barnett and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This is the first in a series of research monographs that focus on the research, development and use of inequalities in probability and statistics. All of the papers have been peer refereed and this first edition covers a range of topics that include both survey material of published work as well as new results appearing in print for the first time.

Advanced Inequalities

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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2010-10-26

Advanced Inequalities written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-26 with Mathematics categories.

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, Gruss and Comparison of Means inequalities are studied.The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

Advanced Inequalities

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Author : George A. Anastassiou
language : en
Publisher: World Scientific
Release Date : 2011

Advanced Inequalities written by George A. Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end. The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and HardyOpial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as ChebyshevGruss, Gruss and Comparison of Means inequalities are studied. The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

Stochastic Inequalities And Applications

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Author : Evariste Gine
language : en
Publisher:
Release Date : 2003-10-24

Stochastic Inequalities And Applications written by Evariste Gine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-24 with categories.

Inequalities In Analysis And Probability

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