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.
This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics.
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.
Limit Theorems In Probability Statistics And Number Theory
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Author : Peter Eichelsbacher
language : en
Publisher: Springer
Release Date : 2013-04-26
Limit Theorems In Probability Statistics And Number Theory written by Peter Eichelsbacher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-26 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.
Martingale Limit Theory And Its Application
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Author : P. Hall
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Martingale Limit Theory And Its Application written by P. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
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.
Information Theory And The Central Limit Theorem
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Author : Oliver Thomas Johnson
language : en
Publisher: World Scientific
Release Date : 2004
Information Theory And The Central Limit Theorem written by Oliver Thomas Johnson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Probability
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-30
Probability written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-30 with Mathematics categories.
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.
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 Mathematics 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.
Mathematical Statistics And Limit Theorems
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Author : Marc Hallin
language : en
Publisher: Springer
Release Date : 2015-04-07
Mathematical Statistics And Limit Theorems written by Marc Hallin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-07 with Mathematics categories.
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.
Probability Theory
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Author : Yuan S. Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Theory written by Yuan S. Chow 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 2012-12-06 with Mathematics categories.
Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub ject, generally attributed to investigations by the renowned French mathe matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).