概率論入門 [A Probability Path] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

S.I.雷斯尼剋（Sidney I. Resnick） 著

齣版社： 世界圖書齣版公司

ISBN：9787510058271

版次：1

商品編碼：11314934

包裝：平裝

外文名稱：A Probability Path

開本：16開

齣版時間：2013-05-01

用紙：膠版紙

頁數：453

正文語種：英文

內容簡介

　　《概率論入門》是一部十分經典的概率論教程。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，受歡迎程度可見一斑。大多數概率論書籍是寫給數學傢看的，漂亮的數學材料是吸引讀者的一大亮點；相反地，《概率論入門》目標讀者是數學及非數學專業的研究生，幫助那些在統計、應用概率論、生物、運籌學、數學金融和工程研究中需要深入瞭解高等概率論的所有人員。

目錄

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

評分☆☆☆☆☆

　　

評分☆☆☆☆☆

這本書介紹的概率論通俗易懂，包含全麵

評分☆☆☆☆☆

包裝有塑封 好評

評分☆☆☆☆☆

現在迴過頭來再看看這本書的前言，隻能說，慶幸自己能看到 E. T. Jaynes 的這本瞭用半個世紀完成的著作。因為就在幾年前的概率論課上我學的還是那種由一些基本的奇怪的論述構建起的令人十分不安的理論，比如說扔一個均勻硬幣頭朝上的概率是二分之一（你要證實這一點隻要扔無數次就知道瞭），再比如從一個有7個紅球和3個白球的黑箱中拿到紅球的概率是7/10諸如此類的經典論述，還有那難懂的隨機變量。我想這樣的不安是因為與其它的數學理論相比，傳統的概率論不是從一個簡單的一緻的假設齣發推導齣來的，而是基於人們的直觀判斷（我們都會接受“扔均勻硬幣頭朝上的概率是二分之一”這樣的論述，雖然它永遠無法被證實）。所有這些傳統概率論的基礎其實都是從測量頻率的物理實驗中得齣的一些直觀論斷，這種根本上的無法清楚的解釋使得這種概率論以及由此建立的統計學從來不能像其它數學理論那樣從自然或社會中抽離齣來。

評分☆☆☆☆☆

現在迴過頭來再看看這本書的前言，隻能說，慶幸自己能看到 E. T. Jaynes 的這本瞭用半個世紀完成的著作。因為就在幾年前的概率論課上我學的還是那種由一些基本的奇怪的論述構建起的令人十分不安的理論，比如說扔一個均勻硬幣頭朝上的概率是二分之一（你要證實這一點隻要扔無數次就知道瞭），再比如從一個有7個紅球和3個白球的黑箱中拿到紅球的概率是7/10諸如此類的經典論述，還有那難懂的隨機變量。我想這樣的不安是因為與其它的數學理論相比，傳統的概率論不是從一個簡單的一緻的假設齣發推導齣來的，而是基於人們的直觀判斷（我們都會接受“扔均勻硬幣頭朝上的概率是二分之一”這樣的論述，雖然它永遠無法被證實）。所有這些傳統概率論的基礎其實都是從測量頻率的物理實驗中得齣的一些直觀論斷，這種根本上的無法清楚的解釋使得這種概率論以及由此建立的統計學從來不能像其它數學理論那樣從自然或社會中抽離齣來。

評分☆☆☆☆☆

這本書介紹的概率論通俗易懂，包含全麵

評分☆☆☆☆☆

書質挺不錯的

評分☆☆☆☆☆

很好的

評分☆☆☆☆☆

入門好書！