random matrices and random partitions normal convergence world scientific series on probability theory and its applications

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Random Matrices And Random Partitions

Author : Zhonggen Su
ISBN : 9789814612241
Genre : Mathematics
File Size : 51. 85 MB
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This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of various eigenvalue statistics. This is attributed to the nice algebraic structures of models. This part also studies the Circular β Ensembles and Hermitian β Ensembles. Part III is devoted to the study of random uniform and Plancherel partitions. There is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models. A remarkable point is the conditioning argument in each model. Through enlarging the probability space, we run into independent geometric random variables as well as determinantal point processes with discrete Bessel kernels. This book treats only second-order normal fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes. Contents:Normal ConvergenceCircular Unitary EnsembleGaussian Unitary EnsembleRandom Uniform PartitionsRandom Plancherel Partitions Readership: Graduates and researchers majoring in probability theory and mathematical statistics, especially for those working on Probability Limit Theory. Key Features:The book treats only two special models of random matrices, that is, Circular and Gaussian Unitary Ensembles, and the focus is on second-order fluctuations of primary eigenvalue statistics. So all theorems and propositions can be stated and proved in a clear and concise languageIn a companion part, the book also treats two special models of random integerpartitions, namely, random uniform and Plancherel partitions. It exhibits a surprising similarity between random matrices and random partitions from the viewpoint of asymptotic distribution theory, though there is no direct link between finite modelsThe limit distributions of most statistics of interest are obtained by reducing to classical central limit theorems for sums of independent random variables, martingale sequences and Markov chains. So the book is easily accessible to readers that are familiar with a standard probability theory textbookKeywords:Central Limit Theorems;Random Matrices;Random Partitions

An Introduction To The Theory Of Probability

Author : Parimal Mukhopadhyay
ISBN : 9789814313421
Genre : Mathematics
File Size : 30. 68 MB
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The Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution and convergence of random variables. Difficult ideas have been explained lucidly and have been augmented with explanatory notes, examples and exercises. The basic requirement for reading this book is simply a knowledge of mathematics at graduate level. This book tries to explain the difficult ideas in the axiomatic approach to the theory of probability in a clear and comprehensible manner. It includes several unusual distributions including the power series distribution that have been covered in great detail. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging. The author is a former Professor of the Indian Statistical Institute, India.

A First Course In Probability And Statistics

Author : B. L. S. Prakasa Rao
ISBN : 9789812836533
Genre : Mathematics
File Size : 45. 11 MB
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This book provides a clear exposition of the theory of probability along with applications in statistics.

Everyday Probability And Statistics

Author : M. M. Woolfson
ISBN : 9781848160330
Genre : Mathematics
File Size : 90. 96 MB
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Probability and statistics impinge on the life of the average person in a variety of ways OCo as is suggested by the title of this book. Very often, information is provided that is factually accurate but intended to present a biased view. This book presents the important results of probability and statistics without making heavy mathematical demands on the reader. It should enable an intelligent reader to properly assess statistical information and to understand that the same information can be presented in different ways.

Ruin Probabilities

Author : S?ren Asmussen
ISBN : 9789814282529
Genre : Mathematics
File Size : 27. 85 MB
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The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cram‚r?Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber?Shiu functions and dependence.

Weak Convergence And Its Applications

Author : Lin Zhengyan
ISBN : 9789814447713
Genre : Mathematics
File Size : 44. 97 MB
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Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory.

Linear Regression Analysis

Author : Xin Yan
ISBN : 9789812834102
Genre : Mathematics
File Size : 61. 48 MB
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"This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.

Probability Theory

Author : Nikolai Dokuchaev
ISBN : 9789814678056
Genre : Business & Economics
File Size : 88. 95 MB
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This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

The Stress Strength Model And Its Generalizations

Author : Samuel Kotz
ISBN : 9812564519
Genre : Mathematics
File Size : 33. 50 MB
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This important book presents developments in a remarkable field ofinquiry in statistical/probability theory the stressOCostrengthmodel.Many papers in the field include the enigmatic words"P"("X"Y") or something similar in thetitle."

Essentials Of Stochastic Finance

Author : Albert N Shiryaev
ISBN : 9789814495660
Genre : Science
File Size : 70. 42 MB
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This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks. Contents:Facts. Models:Main Concepts, Structures, and Instruments. Aims and Problems of Financial Theory and Financial EngineeringStochastic Models. Discrete TimeStochastic Models. Continuous TimeStatistical Analysis of Financial DataTheory:Theory of Arbitrage in Stochastic Financial Models. Discrete TimeTheory of Pricing in Stochastic Financial Models. Discrete TimeTheory of Arbitrage in Stochastic Financial Models. Continuous TimeTheory of Pricing in Stochastic Financial Models. Continuous Time Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos. Keywords:Stochastic Finance;Financial Theory;Financial Engineering;Financial MathematicsReviews: “This is a remarkable text, containing a huge amount of interesting material on modern stochastic finance. Especially the young (novice) researcher in the field will find it a very useful basis of results essential for further research. The set of references is impressive and the level of writing is clear and pedagogically sound … a much more in-depth treatment of a very wide and encompassing range of stochastic models is given. In summary: a text to be recommended warmly.” International Statistical Institute “It is a very comprehensive survey of the results from the theories of stochastic processes, time series and related statistical procedures relevant to finance applications. It also develops classical pricing models and results. It is written in a very lively style, in which the author effortlessly jumps from abstract mathematical frameworks to interesting historical remarks.” Mathematical Reviews “The author's choice of material is outstanding and well worth the time and effort it will require to get through … For anyone interested or working in the field and who have a good mathematical background, this book will be a valuable resource and a rich and stimulating source of intellectual pleasure.” Journal of Applied Mathematics and Stochastic Analysis “… as an encyclopedia of results and methods for financial analysis it is very impressive and certainly very useful as well.” Mathematics Abstracts

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