Download or read book Limit Theorems in Probability Statistics and Number Theory written by Peter Eichelsbacher and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.
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 Limit Theorems in Probability and Statistics written by I. Berkes and published by North Holland. This book was released on 1990 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Heads or Tails written by Emmanuel Lesigne and published by American Mathematical Soc.. This book was released on 2005 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theorems--statements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians,engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition aboutprobability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a one-year undergraduate course in analysis.
Download or read book Limit Theorems in Probability and Statistics written by Pál Révész and published by . This book was released on 1984 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability The Classical Limit Theorems written by Henry McKean and published by Cambridge University Press. This book was released on 2014-11-27 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.
Download or read book Mathematical Statistics and Limit Theorems written by Marc Hallin and published by Springer. This book was released on 2016-10-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.
Download or read book Some Limit Theorems in Statistics written by R. R. Bahadur and published by SIAM. This book was released on 1971-01-01 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff's theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.
Download or read book Uniform Central Limit Theorems written by R. M. Dudley and published by Cambridge University Press. This book was released on 1999-07-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise by an acknowledged expert includes several topics not found in any previous book.
Download or read book Limit Theorems for Randomly Stopped Stochastic Processes written by Dmitriĭ Sergeevich Silʹvestrov and published by Springer Science & Business Media. This book was released on 2004 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes.This volume is the first to present a state-of-the-art overview of this field, with many of the results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast, and technically demanding, Russian literature in detail. A survey of the literature and an extended bibliography of works in the area are also provided.The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area and remain relevant for years to come.
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 Limit Theorems For Associated Random Fields And Related Systems written by Alexander Bulinski and published by World Scientific. This book was released on 2007-09-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
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 The Life and Times of the Central Limit Theorem written by William J. Adams and published by American Mathematical Soc.. This book was released on 2009-11-25 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making. --Philip Peak, The Mathematics Teacher, May, 1975 I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics. --Wei-Ching Chang, Historica Mathematica, August, 1976 In the months since I wrote ... I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics. --Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975 The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of The Life and Times of the Central Limit Theorem, Second Edition traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of $\exp (x^2)$ as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.
Download or read book Probability Theory written by Yakov G. Sinai and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics.
Download or read book Problems in Probability Theory Mathematical Statistics and Theory of Random Functions written by A. A. Sveshnikov and published by Courier Corporation. This book was released on 2012-04-30 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.
