Limit Theorems In Probability Statistics And Number Theory
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Limit Theorems In Probability Statistics And Number Theory
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Author : Peter Eichelsbacher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-23
Limit Theorems In Probability Statistics And Number Theory written by Peter Eichelsbacher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-23 with Mathematics categories.
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.
Limit Theorems Of Probability Theory
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Author : Yu.V. Prokhorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Limit Theorems Of Probability Theory written by Yu.V. Prokhorov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Limit Theorems In Probability And Statistics
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Author : I. Berkes
language : en
Publisher: North Holland
Release Date : 1990
Limit Theorems In Probability And Statistics written by I. Berkes and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The Life And Times Of The Central Limit Theorem
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Author : William J. Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-25
The Life And Times Of The Central Limit Theorem written by William J. Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-25 with Mathematics categories.
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.
Limit Theorems For Associated Random Fields And Related Systems
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Author :
language : en
Publisher:
Release Date :
Limit Theorems For Associated Random Fields And Related Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A History Of The Central Limit Theorem
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Author : Hans Fischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-08
A History Of The Central Limit Theorem written by Hans Fischer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-08 with Mathematics categories.
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.
Some Limit Theorems In Statistics
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Author : R. R. Bahadur
language : en
Publisher: SIAM
Release Date : 1971-01-01
Some Limit Theorems In Statistics written by R. R. Bahadur and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.
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.
Random Summation
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Author : Boris V. Gnedenko
language : en
Publisher: CRC Press
Release Date : 2020-07-24
Random Summation written by Boris V. Gnedenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-24 with Mathematics categories.
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.
Stable Convergence And Stable Limit Theorems
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Author : Erich Häusler
language : en
Publisher: Springer
Release Date : 2015-06-09
Stable Convergence And Stable Limit Theorems written by Erich Häusler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-09 with Mathematics categories.
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Heads Or Tails
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Author : Emmanuel Lesigne
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Heads Or Tails written by Emmanuel Lesigne and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Limit theorems categories.
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.