点击选择搜索分类
首页 - 科学史话- 正文
☆☆☆☆☆
||
S.I.雷斯尼克(Sidney I. Resnick) 著
出版社: 世界图书出版公司 ISBN:9787510058271 版次:1 商品编码:11314934 包装:平装 外文名称:A Probability Path 开本:16开 出版时间:2013-05-01 用纸:胶版纸 页数:453 正文语种:英文
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
概率论入门 [A Probability Path] 电子书 下载 mobi epub pdf txt
概率论入门 [A Probability Path]-so88
概率论入门 [A Probability Path] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
S.I.雷斯尼克(Sidney I. Resnick) 著
出版社: 世界图书出版公司 ISBN:9787510058271 版次:1 商品编码:11314934 包装:平装 外文名称:A Probability Path 开本:16开 出版时间:2013-05-01 用纸:胶版纸 页数:453 正文语种:英文
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
preface1 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] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 第七届艾特奖获奖作品年鉴 国际空间设计大奖艾特奖组
- 包邮 黑旗 isis的崛起 乔比沃里克著 普利策奖获奖作品 惊悚刺激黑暗纪实
- 科学可以这样看丛书:失落的非洲寺庙 9787229126308 [南非] 迈克尔特林格-R
- 【预订】The DevOps Handbook: How to Create
- 2018年暑假读一本好书 海洋生命 与海洋生命面对面 奇妙世界绘本
- 互联网消费金融:模式与实践
- 水文学(第五版)/普通高等教育土建学科专业“十二五”规划教材
- 包邮 [按需印刷]垂直攀登:稻盛和夫的生命智慧与经营哲学 王育琨|194788
- {RT}闻名世界的壮丽瀑布-探索发现丛书编委会编 四川科技出版社 978753647604
- 商城正版 二战经典战役全记录 二战全史大全集 第二次世界大战回忆录 军事系列书籍
- 西南大学史-第四卷
- 国殇大全集 正版 国民党正面战场抗战纪实 完整版16开精装全10卷 纪念中国人民抗日战争
- 科普大讲坛:探索人体奥秘,关爱生命健康
- 【虎彩 按需出版】街头政治与颜色革命 刘明主编 中国传媒大学出版社
- 《物含妙理总堪寻:从爱因斯坦到霍金》