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Titlebook: Probability Essentials; Jean Jacod,Philip Protter Textbook 20001st edition Springer-Verlag Berlin Heidelberg 2000 Brownian motion.Martinga

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发表于 2025-3-21 19:11:47 | 显示全部楼层 |阅读模式
书目名称Probability Essentials
编辑Jean Jacod,Philip Protter
视频video
概述In the words of one reviewer: "Normally graduate students need two books, one on measure theory and one on probability theory..This book contains (most of) the essentials of both fields and students c
丛书名称Universitext
图书封面Titlebook: Probability Essentials;  Jean Jacod,Philip Protter Textbook 20001st edition Springer-Verlag Berlin Heidelberg 2000 Brownian motion.Martinga
描述We present here a one-semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to fill a current need: there are mathematically sophisticated stu­ dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Prob­ ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it difficult to construct a lean one semester course that covers (what we believe are) the essential topics. Chapters 1-23 provide such a course. We have indulged ourselves a bit by including Chapters 24-28 which are highly optional, but which may prove useful to Economists and Electrical Engineers. This book had its origins in a course the second author gave in Perugia, Italy, in 1997; he used the samizdat "notes" of the first author, long used for courses at the University of Paris VI, augmenting them as needed. The result has been further tested at courses given
出版日期Textbook 20001st edition
关键词Brownian motion; Martingal; Martingale; Martingales; Random variable; central limit theorem; conditional p
版次1
doihttps://doi.org/10.1007/978-3-642-51431-9
isbn_ebook978-3-642-51431-9Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 2000
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Convergence of Random Variables,is is called . A random variable is of course a function (.:Ω → . for an abstract space .), and thus we have the same notion: a sequence . → . . lim. .(.), for all .. This natural definition is surprisingly useless in probability. The next example gives an indication why.
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https://doi.org/10.1007/978-3-642-51431-9Brownian motion; Martingal; Martingale; Martingales; Random variable; central limit theorem; conditional p
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Springer-Verlag Berlin Heidelberg 2000
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Conditional Probability and Independence,Let . and . be two events defined on a probability space. Let .(.) denote the number of times . occurs divided by .. Intuitively, as n gets large, .(.) should be close to .. Informally, we should have ..
发表于 2025-3-23 03:39:28 | 显示全部楼层
Probabilities on a Countable Space,For Chapter 4, we assume . is countable, and we take . = 2. (the class of all subsets of .).
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Construction of a Probability Measure,Here we no longer assume . is countable. We assume given . and a .-algebra . ⊂ 2.. (., .) is called a . We want to construct probability measures on . When . is finite or countable we have already-seen this is simple to do. When . is uncountable, the same technique does not work; indeed, a “typical” probability . will have .({.}) = 0 for all .
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