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

　　我想 Jaynes 提齣廣義邏輯的意義在於它可以將概率論（用廣義邏輯來理解，概率論和統計學本質上是沒差的）納入純粹的數學知識體係, 或者說是邏輯推理，這樣就能說得清瞭，就能找到最優解瞭，不像傳統的概率統計學因為不能從一些基本的假設一緻地推導齣來，它的應用總是上下文相關的，人們總是針對一類問題特彆地設定一些直觀的假設，比如關於扔硬幣的問題就假設扔無數次有一半是正麵朝上的而關於從黑箱中拿球的問題又得重新假設拿球無數次有7/10次拿齣的是紅球，總之感覺很不靠譜。可是我們要讓建立的理論有實用價值就必須去研究自然物理或社會經濟的定律，不然就隻是一些空中樓閣裏的思維遊戲，因此我們需要一套方法來分析得到的數據，我們希望建立有實際意義的抽象模型。抽象模型一旦建立，我們就可以進行純粹的抽離的邏輯推理(deductive reasoning)，這是一個自由的快樂的過程，你可以賦予它任何含義而不必理會任何現實環境。試想如果連建立抽象模型的過程(inductive reasoning)也能這樣，那就是神瞭！比如我們想研究現在的通貨膨脹問題，希望能建立起有效的抽象模型（這樣我們就能做預測做優化等等一係列控製），就要采集數據。我們會發現這是一個復雜的過程，因為數據本身未必可信（在物理實驗裏這可能是因為數據裏含有未知的誤差，而在經濟分析中我想這主要是由於人的不確定因素）， 用傳統的狹義邏輯（有效|無效數據）沒辦法建立有效的模型，而廣義邏輯就是用來描述數據（或一個命題，說這一季度的通脹率是多少多少）的可信度(plausibility)的。

評分☆☆☆☆☆

這套書內容都比較深，難度有點大，先買來放著。

評分☆☆☆☆☆

麵嚮非數學專業的入門書，挺好。

評分☆☆☆☆☆

我們這屆第一次用，感覺書中內容很偏基礎，理論有點多，但是質量很高。

評分☆☆☆☆☆

Goooooooooooooooooood

評分☆☆☆☆☆

東西不錯，希望一直好用。

評分☆☆☆☆☆

很好的基於測度論的概率論教材

評分☆☆☆☆☆

很好的基於測度論的概率論教材