Download or read book The Central Limit Theorem for Real and Banach Valued Random Variables written by Aloisio Araujo and published by John Wiley & Sons. This book was released on 1980 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability in Banach Spaces written by Michel Ledoux and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

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 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 Probability in Banach Spaces written by Anatole Beck and published by Springer. This book was released on 2006-11-14 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Probability and Banach Spaces written by Jesus Bastero and published by Springer. This book was released on 2006-12-08 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Approximation Theory in the Central Limit Theorem written by V. Paulauskas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: ~Et mai . ..., si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aIIe.' 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. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities 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'etre of this series.

Download or read book Limit Theorems for Sums of Exchangeable Random Variables written by Robert Lee Taylor and published by Rowman & Littlefield Publishers. This book was released on 1985 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: To find more information about Rowman and Littlefield titles, please visit www.rowmanlittlefield.com.

Download or read book Probability in Banach Spaces III written by A. Beck and published by Springer. This book was released on 2006-11-14 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Uniform Central Limit Theorems written by R. M. Dudley and published by Cambridge University Press. This book was released on 2014-02-24 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.

Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

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 PROBABILITY AND STATISTICS Volume I written by Reinhard Viertl and published by EOLSS Publications. This book was released on 2009-06-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs

Download or read book Probability in Banach Spaces 6 written by Haagerup and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was ar ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material pre sented in the lectures; several results covered have been published else where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these institu tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces. . . . .

Download or read book Probability in Banach Spaces 8 Proceedings of the Eighth International Conference written by R.M. Dudley and published by Springer Science & Business Media. This book was released on 1992-10 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.