测度理论概率导论

本书特色

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《测度理论概率导论(第2版)(英文)》内容有zeta函数，q—zeta函数，相伴级数与积分，微分形式：理论与练习，离散与微分包含的逼近和优化，艾伦·图灵：他的工作与影响，测度理论概率导论（第2版），带有潜在故障恢复系统的半马尔柯夫模型控制，数学分析原理，*偏微分方程的有效动力学，图的谱半径。

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内容简介

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《测度理论概率导论(第2版)(英文)》由哈尔滨工业大学出版社出版。

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目录

目录
Pictured on the Cover Preface to First Edition Preface to Second Edition CHAPTER 1 Certain Classes of Sets， Measurability， and Pointwise Approximation ／／1 1.1 Measurable Spaces ／／1 1.2 Product Measurable Spaces ／／5 1.3 Measurable Functions and Random Variables ／／7 CHAPTER 2 Definition and Construction of a Measure and its Basic Properties ／／19 2.1 About Measures in General， and Probability Measures in Particular ／／19 2.2 Outer Measures ／／22 2.3 The Carathéodory Extension Theorem ／／27 2.4 Measures and （Point） Functions ／／30 CHAPTER 3 Some Modes of Convergence of Sequences of Random Variables and their Relationships ／／41 3.1 Almost Everywhere Convergence and Convergence in Measure ／／41 3.2 Convergence in Measure is Equivalent to Mutual Convergence in Measure ／／45 CHAPTER 4 The Integral of a Random Variable and its Basic Properties ／／55 4.1 Definition of the Integral ／／55 4.2 Basic Properties of the Integral ／／60 4.3 Probability Distributions ／／66 CHAPTER 5 Standard Convergence Theorems，The Fubini Theorem ／／71 5.1 Standard Convergence Theorems and Some of Their Ramifications ／／71 5.2 Sections， Product Measure Theorem，the Fubini Theorem ／／80 5.2.1 Preliminaries for the Fubini Theorem ／／88 CHAPTER 6 Standard Moment and Probability inequalities，Convergence in the rth Mean and its Implications ／／95 6.1 Moment and Probability Inequalities ／／95 6.2 Convergence in the rth Mean，Uniform Continuity，Uniform Integrability，and Their Relationships ／／101 CHAPTER 7 The Hahn—Jordan Decomposition Theorem，The Lebesgue Decomposition Theorem，and the Radon—Nikodym Theorem ／／117 7.1 The Hahn—Jordan Decomposition Theorem ／／117 7.2 The Lebesgue Decomposition Theorem ／／122 7.3 The Radon—Nikodym Theorem ／／128 CHAPTER 8 Distribution Functions and Their Basic Properties，Helly—Bray Type Results ／／135 8.1 Basic Properties of Distribution Functions ／／135 8.2 Weak Convergence and Compactness of a Sequence of Distribution Functions ／／141 8.3 Helly—Bray Type Theorems for Distribution Functions ／／145 CHAPTER 9 Conditional Expectation and Conditional Probability，and Related Properties and Results ／／153 9.1 Definition of Conditional Expectation and Conditional Probability ／／153 9.2 Some Basic Theorems About Conditional Expectations and Conditional Probabilities ／／158 9.3 Convergence Theorems and Inequalities for Conditional Expectations ／／160 9.4 Furth Properties of Conditional Expectations and Conditional Probabilities ／／169 CHAPTER 10 Independence ／／179 10.1 Independence of Events，σ—Fields，and Random Variables ／／179 10.2 Some Auxiliary Results ／／181 10.3hoof of Theorem 1 and of Lemma 1 in Chapter 9 ／／187 CHAPTER 11 Topics from the Theory of Characteristic Functions ／／193 11.1 Definition of the Characteristic Function of a Distribution and Basic Properties ／／193 11.2 The Inversion Formula ／／195 11.3 Convergence in Distribution and Convergence of Characteristic Functions—The Paul Lévy Continuity Theorem／／202 11.4 Convergence in Distribution in the Multidimensional Case—The Cramér’—Wold Device ／／210 11.5 Convolution of Distribution Functions and Related Results ／／211 11.6 Some Further Properties of Characteristic Functions ／／216 11.7 Applications to the Weak Law of Large Numbers and the Central Lirnit Theorem ／／223 11.8 The Moments of a Random Variable Detenmne its Distribution ／／225 11.9 Some Basic Concepts and Results from Complex Analysis Employed in the Proof of Theorem 11 ／／229 CHAPTER 12 The Central limit Problem：The Centered Case ／／239 12.1 Convergence to the Normal Law （Central Limit Theorem，CLT） ／／240 12.2 Limiting Laws of L（Sn） Under Conditions （C） ／／245 12.3 Conditions for the Central Limit Theorem to Hold ／／252 12.4 Proof of Results in Section 12.2 ／／260 CHAPTER 13 The central Limit Problem：The Noncentered Case ／／271 13.1 Notation and Preliminary Discuss1on ／／271 13.2 Limiting Laws of L（Sn） Under COnditions （C”） ／／274 13.3 Two Special Cases of the Limiting Laws of L（Sn） ／／278 CHAPTER 14 Topics from Sequences of Independent Random Variables ／／290 14.1 Kolmogorov Inequalities ／／290 14.2 More Important Results Toward Proving the Strong Law of Large Numbers ／／294 14.3 Statement and proof of the Strong Law of Large Numbers ／／302 14.4 A Version of the Strong Law of Large Numbers for Random Variables with Infinite Expectation ／／309 14.5 Some Further Results on Sequences of Independent Random Variables ／／313 CHAPTER 15 Topics from Ergodic Theory ／／319 15.1 Stochastic Process， the Coordinate Process，Stationary Process，and Related Results ／／320 15.2 Measure—Preserving Transformations，the Shift Transformation，and Related Results ／／323 15.3 Invariant and Almost Sure Invariant Sets Relative to a Transformation，and Related Results ／／326 15.4 Measure—Preserving Ergodic Transformations，Invariant Random Variables Relative to a Transformation， and Related Results ／／331 15.5 The Ergodic Theorem，Preliminary Results ／／332 15.6 Invariant Sets and Random Variables Relative to a Process，Formulation of the Ergodic Theorem in Terms of Stationary Processes，Ergodic Processes ／／340 CHAPTER 16 Two Cases of Statistical Inference：Estimation of a Real—Valued Parameter， Nonparametric Estimation of a Probability Density Function ／／347 16.1 Construction of an Estimate of a Real—Valued Parameter ／／347 16.2 Construction of a Strongly Consistent Estimate of a Real—Valued Parameter ／／348 16.3 Some Preliminary Results ／／351 16.4 Asymptotic Normality of the Strongly Consistent Estimate ／／355 16.5 Nonparametric Estimation of a Probability Density Function ／／364 16.6 Proof of Theorems 3—5 ／／368 APPENDIX A Brief Review of Chapters 1—16 ／／375 APPENDIX B Brief Review of Riemann—Stieltjes Integral ／／385 APPENDIX C Notation and Abbreviations ／／389 Selected Referel1ces ／／391 Index ／／393

封面

书名:测度理论概率导论

作者:(美)罗萨斯(G. G. Roussas

页数:0

定价:¥88.0

出版社:哈尔滨工业大学出版社

出版日期:2016-01-01

ISBN:9787560357614

PDF电子书大小:55MB 高清扫描完整版