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Inequalities in Analysis and Probability

Author: Odile Pons

Publisher: World Scientific

Published: 2016-11-03

Total Pages: 308

ISBN-13: 9813144009

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.

Probability Inequalities

Author: Zhengyan Lin

Publisher: Springer Science & Business Media

Published: 2011-05-30

Total Pages: 192

ISBN-13: 3642052614

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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.

Inequalities in Statistics and Probability

Author: Yung Liang Tong

Publisher: IMS

Published: 1984

Total Pages: 270

ISBN-13: 9780940600041

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Advances in Inequalities from Probability Theory and Statistics

Author: Neil S. Barnett

Publisher: Nova Publishers

Published: 2008

Total Pages: 244

ISBN-13: 9781600219436

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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.

Inequalities In Analysis And Probability

Author: Odile Pons

Publisher: World Scientific

Published: 2012-11-29

Total Pages: 232

ISBN-13: 9814412597

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Inequalities in Analysis and Probability

Author: Odile Pons

Publisher: World Scientific

Published: 2013

Total Pages: 232

ISBN-13: 9814412570

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Inequalities In Analysis And Probability (Third Edition)

Author: Odile Pons

Publisher: World Scientific

Published: 2021-10-18

Total Pages: 371

ISBN-13: 9811231362

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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.

Probability Inequalities in Multivariate Distributions

Author: Y. L. Tong

Publisher: Academic Press

Published: 2014-07-10

Total Pages: 256

ISBN-13: 1483269213

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Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

Inequalities: A Journey into Linear Analysis

Author: D. J. H. Garling

Publisher: Cambridge University Press

Published: 2007-07-05

Total Pages: 347

ISBN-13: 1139465147

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This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

Stochastic Inequalities and Applications

Author: Evariste Giné

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 362

ISBN-13: 3034880693

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Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.