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Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics

Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics Author Zhidong Bai
ISBN-10 9789814579070
Release 2014-01-24
Pages 232
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The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance. Contents:IntroductionLimiting Spectral DistributionsExtreme EigenvaluesCentral Limit Theorems of Linear Spectral StatisticsLimiting Behavior of Eigenmatrix of Sample Covariance MatrixWireless CommunicationsLimiting Performances of Linear and Iterative ReceiversApplication to Finance Readership: Graduate students and researchers in random matrices. Key Features:The book introduces basic theorems in large dimensional random matrices emphasizing those which are established under moment conditions and are thus applicable to statisticsThe long proofs of some theorems are omitted and their references have been providedExamples of various applications to wireless communications and finance are givenKeywords:Statistical Finance;Random Matrix Theory;Spectral Analysis of Random Matrices;Wireless CommunicationsReviews: “Practitioners looking for an introduction to the applications of random matrix theory to finance will find this part useful.” Mathematical Reviews Clippings



Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics

Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics Author Zhidong Bai
ISBN-10 981457905X
Release 2014
Pages 220
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The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.



Spectral Analysis of Large Dimensional Random Matrices

Spectral Analysis of Large Dimensional Random Matrices Author Zhidong Bai
ISBN-10 9781441906618
Release 2009-12-10
Pages 552
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The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.



Probability Inequalities

Probability Inequalities Author Zhengyan Lin
ISBN-10 3642052614
Release 2011-05-30
Pages 181
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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.



Random Matrix Theory and Its Applications

Random Matrix Theory and Its Applications Author Zhidong Bai
ISBN-10 9814273112
Release 2009
Pages 165
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In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications."--pub. desc.



Probability Statistics and Random Processes For Electrical Engineering

Probability  Statistics  and Random Processes For Electrical Engineering Author Alberto Leon-Garcia
ISBN-10 9780133002577
Release 2011-11-21
Pages 832
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This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. This is the standard textbook for courses on probability and statistics, not substantially updated. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples. In this edition, the Computer Methods sections have been updated and substantially enhanced and new problems have been added.



Geometric Properties for Parabolic and Elliptic PDE s

Geometric Properties for Parabolic and Elliptic PDE s Author Rolando Magnanini
ISBN-10 9788847028418
Release 2012-11-27
Pages 292
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The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.



Large Sample Covariance Matrices and High Dimensional Data Analysis

Large Sample Covariance Matrices and High Dimensional Data Analysis Author Jianfeng Yao
ISBN-10 9781107065178
Release 2015-03-26
Pages 322
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Written by leading experts in the field, this book presents the most recent developments in the use of random matrix theory in high-dimensional statistics.



Inequalities in Analysis and Probability

Inequalities in Analysis and Probability Author Odile Pons
ISBN-10 9789813144002
Release 2016-11-03
Pages 308
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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.



Random Walk in Random and Non random Environments

Random Walk in Random and Non random Environments Author P l R‚v‚sz
ISBN-10 9789814447515
Release 2013
Pages 421
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The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results OCo mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.



The Oxford Handbook of Random Matrix Theory

The Oxford Handbook of Random Matrix Theory Author Gernot Akemann
ISBN-10 0198744196
Release 2015-08-01
Pages 952
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With a foreword by Freeman Dyson, the Oxford Handbook of Random Matrix Theory brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In the first part of this book, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicasor supersymmetry. Further, all main



Nonlinear Perron Frobenius Theory

Nonlinear Perron Frobenius Theory Author Bas Lemmens
ISBN-10 9780521898812
Release 2012-05-03
Pages 323
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"Sometimes in mathematics an innocent-looking observation opens up a new road to a fertile field. A nice example of such an observation is due to Garrett Birkhoff [23] and Hans Samelson [187], who remarked that one can use Hilbert's (projective) metric and the contraction mapping principle to prove some of the theorems of Perron and Frobenius concerning eigenvectors and eigenvalues of nonnegative matrices. This idea has been pivotal for the development of nonlinear Perron-Frobenius theory"--



Ranked Set Sampling

Ranked Set Sampling Author Zehua Chen
ISBN-10 9780387216645
Release 2013-03-09
Pages 227
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The first book on the concept and applications of ranked set sampling. It provides a comprehensive review of the literature, and it includes many new results and novel applications. The detailed description of various methods illustrated by real or simulated data makes it useful for scientists and practitioners in application areas such as agriculture, forestry, sociology, ecological and environmental science, and medical studies. It can serve as a reference book and as a textbook for a short course at the graduate level.



Nano Devices and Sensors

Nano Devices and Sensors Author Juin J. Liou
ISBN-10 9781501501555
Release 2016-04-25
Pages 228
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This volume on semiconductor devices focuses on such topics as nano-imprinting, lithography, nanowire charge-trapping, thermo-stability in nanowires, nano-electrodes, and voltage and materials used for fabricating and improving electrical characteristics of nano-materials.



Wireless Broadband Networks

Wireless Broadband Networks Author David T. Wong
ISBN-10 0470434937
Release 2009-04-01
Pages 500
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An introduction to theories and applications in wireless broadband networks As wireless broadband networks evolve into future generation wireless networks, it's important for students, researchers, and professionals to have a solid understanding of their underlying theories and practical applications. Divided into two parts, the book presents: Enabling Technologies for Wireless Broadband Networks—orthogonal frequency-division multiplexing and other block-based transmissions; multi-input/multi-output antenna systems; ultra-wideband; medium access control; mobility resource management; routing protocols for multi-hop wireless broadband networks; radio resource management for wireless broadband networks; and quality of service for multimedia services Systems for Wireless Broadband Networks—long-term evolution cellular networks; wireless broadband networking with WiMax; wireless local area networks; wireless personal area networks; and convergence of networks Each chapter begins with an introduction and ends with a summary, appendix, and a list of resources for readers who would like to explore the subjects in greater depth. The book is an ideal resource for researchers in electrical engineering and computer science and an excellent textbook for electrical engineering and computer science courses at the advanced undergraduate and graduate levels.



Digital Transmission

Digital Transmission Author Dayan Adionel Guimaraes
ISBN-10 3642013597
Release 2010-01-18
Pages 863
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Digital Transmission – A Simulation-Aided Introduction with VisSim/Comm is a book in which basic principles of digital communication, mainly pertaining to the physical layer, are emphasized. Nevertheless, these principles can serve as the fundamentals that will help the reader to understand more advanced topics and the associated technology. In this book, each topic is addressed in two different and complementary ways: theoretically and by simulation. The theoretical approach encompasses common subjects covering principles of digital transmission, like notions of probability and stochastic processes, signals and systems, baseband and passband signaling, signal-space representation, spread spectrum, multi-carrier and ultra wideband transmission, carrier and symbol-timing recovery, information theory and error-correcting codes. The simulation approach revisits the same subjects, focusing on the capabilities of the communication system simulation software VisSim/Comm on helping the reader to fulfill the gap between the theory and its practical meaning. The presentation of the theory is made easier with the help of 357 illustrations. A total of 101 simulation files supplied in the accompanying CD support the simulation-oriented approach. A full evaluation version and a viewer-only version of VisSim/Comm are also supplied in the CD.



An Introduction to Random Matrices

An Introduction to Random Matrices Author Greg W. Anderson
ISBN-10 9780521194525
Release 2010
Pages 492
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A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.