Download or read book Limit Theory for Mixing Dependent Random Variables written by Lin Zhengyan and published by Springer Science & Business Media. This book was released on 1997-07-31 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many practical problems, observations are not independent. In this book, limit behaviour of an important kind of dependent random variables, the so-called mixing random variables, is studied. Many profound results are given, which cover recent developments in this subject, such as basic properties of mixing variables, powerful probability and moment inequalities, weak convergence and strong convergence (approximation), limit behaviour of some statistics with a mixing sample, and many useful tools are provided. Audience: This volume will be of interest to researchers and graduate students in the field of probability and statistics, whose work involves dependent data (variables).
Download or read book Asymptotic Theory of Weakly Dependent Random Processes written by Emmanuel Rio and published by Springer. This book was released on 2017-04-13 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ces notes sont consacrées aux inégalités et aux théorèmes limites classiques pour les suites de variables aléatoires absolument régulières ou fortement mélangeantes au sens de Rosenblatt. Le but poursuivi est de donner des outils techniques pour l'étude des processus faiblement dépendants aux statisticiens ou aux probabilistes travaillant sur ces processus.
Download or read book Dependence in Probability and Statistics written by Eberlein and published by Birkhäuser. This book was released on 1986 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Information Theory and the Central Limit Theorem written by Oliver Thomas Johnson and published by World Scientific. This book was released on 2004 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Download or read book Dependence in Probability and Statistics written by Paul Doukhan and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.
Download or read book Limit Theorems for Large Deviations written by L. Saulis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series
Download or read book Stochastic Limit Theory written by James Davidson and published by Oxford University Press. This book was released on 1994 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a coherent account of recent contributions to limit theory, with particular emphasis on the issues of date dependence and heterogeneity. The book also provides a grounding in the requisite mathematics and probability theory.
Download or read book Independent and Stationary Sequences of Random Variables written by Ilʹdar Abdulovich Ibragimov and published by . This book was released on 1971 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weak Dependence With Examples and Applications written by Jérome Dedecker and published by Springer Science & Business Media. This book was released on 2007-07-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.
Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book Sums of Independent Random Variables written by V.V. Petrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity
Download or read book Convergence of Probability Measures written by Patrick Billingsley and published by John Wiley & Sons. This book was released on 2013-06-25 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.
Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
