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

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[美] 凯罗勒夫（Leonid B.Koralov） 著

出版社： 世界图书出版公司

ISBN：9787510044106

版次：2

商品编码：11124548

包装：平装

外文名称：Theory of Probability and Random Processes

开本：24开

出版时间：2012-06-01

用纸：胶版纸

页数：353

正文语种：英文

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

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本书是动力系统大师sinai的讲义，sinai虽说是搞动力系统的，但他的工作与统计力学，及动力系统统计性质有密切关系，股本书应该也算行家力作。sinai,俄国数学家，生于莫斯科．1953年进入莫斯科大学学习，1957年毕业．1960年获副博士学位，1963年获博士学位，其后留校研究，1971年升任教授．1971年起任苏联科学院Landau理论物理研究所研究员．1993年起兼任美国普林斯顿大学教授．

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很好的教材，赞一个！

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本书为英文原版内容不错，对学习数学有很大帮助，是本不错的工具书，同时有助于提高英语水平，但是发货的包装对书的保护严重不足。

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正版图书，内容经典，不错。

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随机过程

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这个概率论我本科的时候没学好，现在补一补

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送不了就别卖，好好一本书被弄成这样，看着都心疼

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好书好书好书好书好书好书好书好书

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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。