Probabilistic Inequalities
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Author | : George A Anastassiou |
Publisher | : World Scientific |
Total Pages | : 429 |
Release | : 2009-08-11 |
Genre | : Mathematics |
ISBN | : 9814467138 |
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.
Author | : Zhengyan Lin |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2011-05-30 |
Genre | : Mathematics |
ISBN | : 3642052614 |
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.
Author | : Stéphane Boucheron |
Publisher | : Oxford University Press |
Total Pages | : 492 |
Release | : 2013-02-07 |
Genre | : Mathematics |
ISBN | : 0199535256 |
Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.
Author | : Roman Vershynin |
Publisher | : Cambridge University Press |
Total Pages | : 299 |
Release | : 2018-09-27 |
Genre | : Business & Economics |
ISBN | : 1108415199 |
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author | : Yung Liang Tong |
Publisher | : IMS |
Total Pages | : 270 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 9780940600041 |
Author | : Evariste Giné |
Publisher | : Birkhäuser |
Total Pages | : 362 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880693 |
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.
Author | : Oded Goldreich |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662125218 |
Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
Author | : Roberto Tempo |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2004-09-28 |
Genre | : Computers |
ISBN | : 9781852335243 |
Moving on from earlier stochastic and robust control paradigms, this book introduces the fundamentals of probabilistic methods in the analysis and design of uncertain systems. The use of randomized algorithms, guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H-infinity control. Features: • self-contained treatment explaining randomized algorithms from their genesis in the principles of probability theory to their use for robust analysis and controller synthesis; • comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining independent and identically distributed samples; • applications in congestion control of high-speed communications networks and the stability of quantized sampled-data systems. This monograph will be of interest to theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.
Author | : Evarist Giné |
Publisher | : IMS |
Total Pages | : 288 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9780940600676 |
Author | : Alexander S. Poznyak |
Publisher | : Elsevier |
Total Pages | : 568 |
Release | : 2009-08-13 |
Genre | : Technology & Engineering |
ISBN | : 0080914039 |
Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers. The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle. Provides comprehensive theory of matrices, real, complex and functional analysis Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications Contains worked proofs of all theorems and propositions presented