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＜電子ブック＞
A History of the Central Limit Theorem : From Classical to Modern Probability Theory / by Hans Fischer
(Sources and Studies in the History of Mathematics and Physical Sciences. ISSN:21968829)

版	1st ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XVI, 402 p : online resource
著者標目	*Fischer, Hans author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:History LCSH:Probabilities LCSH:Statistics  FREE:History of Mathematical Sciences FREE:Probability Theory FREE:Statistics
一般注記	Preface -- Introduction -- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods -- The hypothesis of elementary errors -- Chebyshev's and markov's contributions -- The way towards modern probability -- General limit problems -- Conclusion: the central limit theorem as a link between classical and modern probability -- Index -- Bibliography This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context HTTP:URL=https://doi.org/10.1007/978-0-387-87857-7

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