概率论和随机过程（第2版） [Theory of Probability and Random Processes] 下载 mobi epub pdf 电子书 2025

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内容简介

This book is primarily based on a one-year course that has been taught for a number of years at Princeton University to advanced undergraduate and graduate students. During the last year a similar course has also been taught at the University of Maryland.
We would like to express our thanks to Ms. Sophie Lucas and Prof. Rafael Herrera who read the manuscript and suggested many corrections. We are particularly grateful to Prof. Boris Gurevich for making many important sug-gestions on both the mathematical content and style.
While writing this book， L. Koralov was supported by a National Sci-ence Foundation grant （DMS-0405152）. Y. Sinai was supported by a National Science Foundation grant （DMS-0600996）.

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目录

Part Ⅰ Probability Theory
1 Random Variables and Their Distributions
1.1 Spaces of Elementary Outcomes， a-Algebras， and Measures
1.2 Expectation and Variance of Random Variables on a Discrete Probability Space
1.3 Probability of a Union of Events
1.4 Equivalent Formulations of a-Additivity， Borel a-Algebras and Measurability
1.5 Distribution Functions and Densities
1.6 Problems
2 Sequences of Independent Trials
2.1 Law of Large Numbers and Applications
2.2 de Moivre-Laplace Limit Theorem and Applications
2.3 Poisson Limit Theorem.
2.4 Problems
3 Lebesgue Integral and Mathematical Expectation
3.1 Definition of the Lebesgue Integral
3.2 Induced Measures and Distribution Functions
3.3 Types of Measures and Distribution Functions
3.4 Remarks on the Construction of the Lebesgue Measure
3.5 Convergence of Functions， Their Integrals， and the Fubini Theorem
3.6 Signed Measures and the R，adon-Nikodym Theorem
3.7 Lp Spaces
3.8 Monte Carlo Method
3.9 Problems
4 Conditional Probabilities and Independence
4.1 Conditional Probabilities
4.2 Independence of Events， Algebras， and Random Variables
4.3
4.4 Problems
5 Markov Chains with a Finite Number of States
5.1 Stochastic Matrices
5.2 Markov Chains
5.3 Ergodic and Non-Ergodic Markov Chains
5.4 Law of Large Numbers and the Entropy of a Markov Chain
5.5 Products of Positive Matrices
5.6 General Markov Chains and the Doeblin Condition
5.7 Problems
6 Random Walks on the Lattice Zd
6.1 Recurrent and Transient R，andom Walks
6.2 Random Walk on Z and the Refiection Principle
6.3 Arcsine Law
6.4 Gambler's Ruin Problem
6.5 Problems
7 Laws of Larze Numbers
7.1 Definitions， the Borel-Cantelli Lemmas， and the Kolmogorov Inequality
7.2 Kolmogorov Theorems on the Strong Law of Large Numbers
7.3 Problems
8 Weak Converaence of Measures
8.1 Defnition of Weak Convergence
8.2 Weak Convergence and Distribution Functions
8.3 Weak Compactness， Tightness， and the Prokhorov Theorem
8.4 Problems
9 Characteristic Functions
9.1 Definition and Basic Properties
9.2 Characteristic Functions and Weak Convergence
9.3 Gaussian Random Vectors
9.4 Problems
10 Limit Theorems
10.1 Central Limit Theorem， the Lindeberg Condition
10.2 Local Limit Theorem
10.3 Central Limit Theorem and Renormalization GrOUD Theorv
10.4 Probabilities of Large Deviations
……
Part Ⅱ Random Processes
Index

前言/序言

概率论和随机过程（第2版） [Theory of Probability and Random Processes] 下载 mobi epub pdf txt 电子书 格式

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随机过程

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老板，没有清单。。。。这个需要给一个，否则不好报销

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随机过程

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首页有个黄色斑。书很专业，是我期待的。

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好书。简单全面。易有所得。oh yeah

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Gooooooooooooooooooooooood

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　　 读者对象：数学及相关专业的大学高年级学生和研究生。

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Gooooooooooooooooooooooood

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他是俄国科学院院士及美国文理科学院院士，他还是伦敦数学会名誉会员．他曾荣获Boltzmann金质奖章（1986）；Heinemann奖（1989）；Markov奖（1990）以及意大利Trieste国际理论物理中心Dirac奖章（1992）．1997年因“对统计力学中数学严格方法及动力系统的遍历理论以及它们在物理学中的应用所做的基本贡献”而获Wolf奖.他的工作是特别令人印象深刻的广度。 “[西奈半岛的工作除了其持久的影响在纯数学]已经起到了至关重要的作用创造动力的混乱，这已经被极其重要的物理学和非线性科学的发展在过去的三概念五年“。引用注意到压倒性的影响西奈半岛的工作，在过去的半个世纪中，包括他的250多篇研究论文，他的几本书。他监督了50多个博士生，其中许多人已成为在自己的权利领域的领导者。引用的结论是，“斯蒂尔被授予终身成就奖西奈承认所有这些成就。

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