Advances In Probability Theory Limit Theorems For Sums Of Random Variables
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Advances In Probability Theory
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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher:
Release Date : 1984
Advances In Probability Theory written by Aleksandr Alekseevich Borovkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Limit theorems (Probability theory). categories.
Advances In Probability Theory Limit Theorems For Sums Of Random Variables
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Author : Aleksandr A. Borovkov
language : en
Publisher:
Release Date : 1985
Advances In Probability Theory Limit Theorems For Sums Of Random Variables written by Aleksandr A. Borovkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Limit theorems (Probability theory) categories.
Advances In Probability Theory
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Author : A. V. Balakrishnan
language : en
Publisher: Springer
Release Date : 1985
Advances In Probability Theory written by A. V. Balakrishnan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Limit theorems (Probability theory). categories.
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.
Limit Theorems For Sums Of Random Variables
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Author : Aleksandr Alekseevič Borovkov (Mathématicien, Russie)
language : en
Publisher:
Release Date : 1985
Limit Theorems For Sums Of Random Variables written by Aleksandr Alekseevič Borovkov (Mathématicien, Russie) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Sums Of Independent Random Variables
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Author : V.V. Petrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sums Of Independent Random Variables written by V.V. Petrov 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.
The classic "Limit Distributions for Sums of Independent Random Variables" 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 Ibragimov y Linnik, "Independent and stationary sequences of random variables", 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
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.
Advanced Probability Theory Second Edition
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Author : Janos Galambos
language : en
Publisher: CRC Press
Release Date : 2023-07-21
Advanced Probability Theory Second Edition written by Janos Galambos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Mathematics categories.
This work thoroughly covers the concepts and main results of probability theory, from its fundamental principles to advanced applications. This edition provides examples early in the text of practical problems such as the safety of a piece of engineering equipment or the inevitability of wrong conclusions in seemingly accurate medical tests for AIDS and cancer.
Uniform Limit Theorems For Sums Of Independent Random Variables
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Author : Taĭvo Viktorovich Arak
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Uniform Limit Theorems For Sums Of Independent Random Variables written by Taĭvo Viktorovich Arak 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 1988 with Mathematics categories.
Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. In the study of even this comparatively simple scheme it is possible to become familiar with the fundamental regularities characterizing the cumulative influence of a large number of random factors. Further, this abstract model is useful in many important practical situations. This book is devoted to the study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions. The authors assume either that the distributions of the terms are concentrated on some finite interval to within a small mass, or that all the terms have the same, but arbitrary, distribution (or other conditions not connected with moment restrictions are introduced). Surprisingly, very substantive results are possible even under such a general statement of the problems.
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.