Limit Theorems of Probability Theory

Limit Theorems of Probability Theory

Author: Yu.V. Prokhorov

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 280

ISBN-13: 3662041723

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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.


A History of the Central Limit Theorem

A History of the Central Limit Theorem

Author: Hans Fischer

Publisher: Springer Science & Business Media

Published: 2010-10-08

Total Pages: 415

ISBN-13: 0387878572

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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.


Mathematical Statistics and Limit Theorems

Mathematical Statistics and Limit Theorems

Author: Marc Hallin

Publisher: Springer

Published: 2015-04-07

Total Pages: 326

ISBN-13: 3319124420

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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: The Classical Limit Theorems

Probability: The Classical Limit Theorems

Author: Henry McKean

Publisher: Cambridge University Press

Published: 2014-11-27

Total Pages: 487

ISBN-13: 1107053218

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A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.


Limit Theorems for Randomly Stopped Stochastic Processes

Limit Theorems for Randomly Stopped Stochastic Processes

Author: Dmitriĭ Sergeevich Silʹvestrov

Publisher: Springer Science & Business Media

Published: 2004

Total Pages: 426

ISBN-13: 9781852337773

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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.


Some Limit Theorems in Statistics

Some Limit Theorems in Statistics

Author: R. R. Bahadur

Publisher: SIAM

Published: 1971-01-01

Total Pages: 48

ISBN-13: 9781611970630

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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.


Probability

Probability

Author: Rick Durrett

Publisher: Cambridge University Press

Published: 2010-08-30

Total Pages:

ISBN-13: 113949113X

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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.