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

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

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

评分☆☆☆☆☆

　　我想 Jaynes 提出广义逻辑的意义在于它可以将概率论（用广义逻辑来理解，概率论和统计学本质上是没差的）纳入纯粹的数学知识体系, 或者说是逻辑推理，这样就能说得清了，就能找到最优解了，不像传统的概率统计学因为不能从一些基本的假设一致地推导出来，它的应用总是上下文相关的，人们总是针对一类问题特别地设定一些直观的假设，比如关于扔硬币的问题就假设扔无数次有一半是正面朝上的而关于从黑箱中拿球的问题又得重新假设拿球无数次有7/10次拿出的是红球，总之感觉很不靠谱。可是我们要让建立的理论有实用价值就必须去研究自然物理或社会经济的定律，不然就只是一些空中楼阁里的思维游戏，因此我们需要一套方法来分析得到的数据，我们希望建立有实际意义的抽象模型。抽象模型一旦建立，我们就可以进行纯粹的抽离的逻辑推理(deductive reasoning)，这是一个自由的快乐的过程，你可以赋予它任何含义而不必理会任何现实环境。试想如果连建立抽象模型的过程(inductive reasoning)也能这样，那就是神了！比如我们想研究现在的通货膨胀问题，希望能建立起有效的抽象模型（这样我们就能做预测做优化等等一系列控制），就要采集数据。我们会发现这是一个复杂的过程，因为数据本身未必可信（在物理实验里这可能是因为数据里含有未知的误差，而在经济分析中我想这主要是由于人的不确定因素）， 用传统的狭义逻辑（有效|无效数据）没办法建立有效的模型，而广义逻辑就是用来描述数据（或一个命题，说这一季度的通胀率是多少多少）的可信度(plausibility)的。

评分☆☆☆☆☆

。。。。。。。。。。

评分☆☆☆☆☆

东西不错，希望一直好用。

评分☆☆☆☆☆

这本书介绍的概率论通俗易懂，包含全面

评分☆☆☆☆☆

Goooooooooooooooooood

评分☆☆☆☆☆

包装很好，还没开始看

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☆☆☆☆☆

面向非数学专业的入门书，挺好。

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