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Titlebook: Probability: A Graduate Course; Allan Gut Textbook 2013Latest edition Springer Science+Business Media New York 2013 Central Limit Theorem.

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发表于 2025-3-21 19:01:19 | 显示全部楼层 |阅读模式
书目名称Probability: A Graduate Course
编辑Allan Gut
视频video
概述Covers probability from a very applied perspective.Many exercises involve mathematical modeling of random phenomena in very practical fields, including insurance/actuarial and the life sciences/biomed
丛书名称Springer Texts in Statistics
图书封面Titlebook: Probability: A Graduate Course;  Allan Gut Textbook 2013Latest edition Springer Science+Business Media New York 2013 Central Limit Theorem.
描述.Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references..
出版日期Textbook 2013Latest edition
关键词Central Limit Theorem; Convergence; Law of Large Numbers; Law of the Iterated Logarithm; Martingales
版次2
doihttps://doi.org/10.1007/978-1-4614-4708-5
isbn_softcover978-1-4899-9755-5
isbn_ebook978-1-4614-4708-5Series ISSN 1431-875X Series E-ISSN 2197-4136
issn_series 1431-875X
copyrightSpringer Science+Business Media New York 2013
The information of publication is updating

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发表于 2025-3-21 22:14:19 | 显示全部楼层
The Law of Large Numbers,Wehavementioned (more than once) that the basis for probabilistic modeling is the stabilization of the relative frequencies.
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https://doi.org/10.1007/978-1-4614-4708-5Central Limit Theorem; Convergence; Law of Large Numbers; Law of the Iterated Logarithm; Martingales
发表于 2025-3-22 21:24:29 | 显示全部楼层
Introductory Measure Theory, probability theory is ., which is concerned with creating principles, methods, and criteria in order to treat data pertaining to such (random) phenomena or data from experiments and other observations of the real world, by using, for example, the theories and knowledge available from the theory of probability.
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The Law of the Iterated Logarithm,ccur, and will occur, one might try to bound the magnitude in some manner. This is what the law of the iterated logarithm (LIL) does, in that it provides a parabolic bound on how large the oscillations of the partial sums may be as a function of the number of summands.
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