概率论入门 [A Probability Path] 下载 mobi epub pdf 电子书 2024

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内容简介

　　《概率论入门》是一部十分经典的概率论教程。1999年初版，2001年第2次重印，2003年第3次重印，同年第4次重印，2005年第5次重印，受欢迎程度可见一斑。大多数概率论书籍是写给数学家看的，漂亮的数学材料是吸引读者的一大亮点；相反地，《概率论入门》目标读者是数学及非数学专业的研究生，帮助那些在统计、应用概率论、生物、运筹学、数学金融和工程研究中需要深入了解高等概率论的所有人员。

目录

preface
1 sets and events
1.1 introduction
1.2 basic set theory
1.2.1 indicator functions
1.3 limits of sets
1.4 monotone sequences
1.5 set operations and closure
1.5.1 examples
1.6 the a-field generated by a given class c
1.7 bore1 sets on the real line
1.8 comparing borel sets
1.9 exercises

2 probability spaces
2.1 basic definitions and properties
2.2 more on closure
2.2.1 dynkin's theorem
2.2.2 proof of dynkin's theorem
2.3 two constructions
2.4 constructions of probability spaces
2.4.1 general construction of a probability model
2.4.2 proof of the second extension theorem
2.5 measure constructions
2.5.1 lebesgue measure on （0， 1）
2.5.2 construction of a probability measure on r with given distribution function f （x）
2.6 exercises

3 random variables， elements， and measurable maps
3.1 inverse maps
3.2 measurable maps， random elements，induced probability measures
3.2.1 composition
3.2.2 random elements of metric spaces
3.2.3 measurability and continuity
3.2.4 measurability and limits
3.3 σ-fields generated by maps
3.4 exercises

4 independence
4.1 basic definitions
4.2 independent random variables
4.3 two examples of independence
4.3.1 records， ranks， renyi theorem
4.3.2 dyadic expansions of uniform random numbers
4.4 more on independence： groupings
4.5 independence， zero-one laws， borel-cantelli lemma
4.5.1 borel-cantelli lemma
4.5.2 borel zero-one law
4.5.3 kolmogorov zero-one law
4.6 exercises

5 integration and expectation
5.1 preparation for integration
5.1.1 simple functions
5.1.2 measurability and simple functions
5.2 expectation and integration
5.2.1 expectation of simple functions
5.2.2 extension of the definition
5.2.3 basic properties of expectation
5.3 limits and integrals
5.4 indefinite integrals
5.5 the transformation theorem and densities
5.5.1 expectation is always an integral on r
5.5.2 densities
5.6 the riemann vs lebesgue integral
5.7 product spaces
5.8 probability measures on product spaces
5.9 fubini's theorem
5.10 exercises

6 convergence concepts
6.1 almost sure convergence
6.2 convergence in probability
6.2.1 statistical terminology
6.3 connections between a.s. and j.p. convergence
6.4 quantile estimation
6.5 lp convergence
6.5.1 uniform integrability
6.5.2 interlude： a review of inequalities
6.6 more on lp convergence
6.7 exercises

7 laws of large numbers and sums of independent random variables
7.1 truncation and equivalence
7.2 a general weak law of large numbers
7.3 almost sure convergence of sums of independent random variables
7.4 strong laws of large numbers
7.4.1 two examples
7.5 the strong law of large numbers for lid sequences
7.5.1 two applications of the slln
7.6 the kolmogorov three series theorem
7.6.1 necessity of the kolmogorov three series theorem
7.7 exercises

8 convergence in distribution
8.1 basic definitions
8.2 scheff6's lemma
8.2.1 scheff6's lemma and order statistics
8.3 the baby skorohod theorem
8.3.1 the delta method
8.4 weak convergence equivalences； portmanteau theorem
8.5 more relations among modes of convergence
8.6 new convergences from old
8.6.1 example： the central limit theorem for m-dependent random variables
8.7 the convergence to types theorem
8.7.1 application of convergence to types： limit distributions for extremes
8.8 exercises

9 characteristic functions and the central limit theorem
9.1 review of moment generating functions and the central limit theorem
9.2 characteristic functions： definition and first properties.
9.3 expansions
9.3.1 expansion of eix
9.4 moments and derivatives
9.5 two big theorems： uniqueness and continuity
9.6 the selection theorem， tightness， and prohorov's theorem
9.6.1 the selection theorem
9.6.2 tightness， relative compactness， and prohorov's theorem
9.6.3 proof of the continuity theorem
9.7 the classical clt for iid random variables
9.8 the lindeberg-feller clt
9.9 exercises

10 martingales
10.1 prelude to conditional expectation：the radon-nikodym theorem
10.2 definition of conditional expectation
10.3 properties of conditional expectation
10.4 martingales
10.5 examples of martingales
10.6 connections between martingales and submartingales
10.6.1 doob's decomposition
10.7 stopping times
10.8 positive super martingales
10.8.1 operations on supermartingales
10.8.2 upcrossings
10.8.3 boundedness properties
10.8.4 convergence of positive super martingales
10.8.5 closure
10.8.6 stopping supermartingales
10.9 examples
10.9.1 gambler's ruin
10.9.2 branching processes
10.9.3 some differentiation theory
10.10 martingale and submartingale convergence
10.10.1 krickeberg decomposition
10.10.2 doob's （sub）martingale convergence theorem
10.11 regularity and closure
10.12 regularity and stopping
10.13 stopping theorems
10.14 wald's identity and random walks
10.14.1 the basic martingales
10.14.2 regular stopping times
10.14.3 examples of integrable stopping times
10.14.4 the simple random walk
10.15 reversed martingales
10.16 fundamental theorems of mathematical finance
10.16.1 a simple market model
10.16.2 admissible strategies and arbitrage
10.16.3 arbitrage and martingales
10.16.4 complete markets
10.16.5 option pricing
10.17 exercises
references
index

前言/序言

概率论入门 [A Probability Path] 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

现在回过头来再看看这本书的前言，只能说，庆幸自己能看到 E. T. Jaynes 的这本了用半个世纪完成的著作。因为就在几年前的概率论课上我学的还是那种由一些基本的奇怪的论述构建起的令人十分不安的理论，比如说扔一个均匀硬币头朝上的概率是二分之一（你要证实这一点只要扔无数次就知道了），再比如从一个有7个红球和3个白球的黑箱中拿到红球的概率是7/10诸如此类的经典论述，还有那难懂的随机变量。我想这样的不安是因为与其它的数学理论相比，传统的概率论不是从一个简单的一致的假设出发推导出来的，而是基于人们的直观判断（我们都会接受“扔均匀硬币头朝上的概率是二分之一”这样的论述，虽然它永远无法被证实）。所有这些传统概率论的基础其实都是从测量频率的物理实验中得出的一些直观论断，这种根本上的无法清楚的解释使得这种概率论以及由此建立的统计学从来不能像其它数学理论那样从自然或社会中抽离出来。

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Goooooooooooooooooood

评分☆☆☆☆☆

还没看，看了来追加，看了来追加

评分☆☆☆☆☆

不错的书，比较适合自己，内容很详细

评分☆☆☆☆☆

我们这届第一次用，感觉书中内容很偏基础，理论有点多，但是质量很高。

评分☆☆☆☆☆

现在回过头来再看看这本书的前言，只能说，庆幸自己能看到 E. T. Jaynes 的这本了用半个世纪完成的著作。因为就在几年前的概率论课上我学的还是那种由一些基本的奇怪的论述构建起的令人十分不安的理论，比如说扔一个均匀硬币头朝上的概率是二分之一（你要证实这一点只要扔无数次就知道了），再比如从一个有7个红球和3个白球的黑箱中拿到红球的概率是7/10诸如此类的经典论述，还有那难懂的随机变量。我想这样的不安是因为与其它的数学理论相比，传统的概率论不是从一个简单的一致的假设出发推导出来的，而是基于人们的直观判断（我们都会接受“扔均匀硬币头朝上的概率是二分之一”这样的论述，虽然它永远无法被证实）。所有这些传统概率论的基础其实都是从测量频率的物理实验中得出的一些直观论断，这种根本上的无法清楚的解释使得这种概率论以及由此建立的统计学从来不能像其它数学理论那样从自然或社会中抽离出来。

评分☆☆☆☆☆

还没看，看了来追加，看了来追加

评分☆☆☆☆☆

不错的书，比较适合自己，内容很详细

评分☆☆☆☆☆

集合和测度论基础，Lebesgue积分，属于概率论的一部中阶教材。

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