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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　　 目次：全书其有四部分，新增加了5章，总共17章。（一）集合论、实数和微积分：集合论；实数体系和微积分。（二）测度、积分和微分：实线上的勒贝格理论；实线上的勒贝格积分；测度和乘积测度的扩展；概率论基础；微分和绝对连续；单测度和复测度。（三）拓扑、度量和正规空间：拓扑、度量和正规空间基本理论；可分离性和紧性；完全空间和紧空间；希尔伯特空间和经典巴拿赫空间；正规空间和局部凸空间。（四）调和分析、动力系统和hausdorff侧都：调和分析基础；可测动力系统；hausdorff测度和分形。

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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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不错是想要的书，比较经典

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影印版的真的特别好！其实应该多读一点这种真正的原著！

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数学上的随机过程是由实际随机过程概念引起的一种数学结构。人们研究这种过程，是因为它是实际随机过程的数学模型，或者是因为它的内在数学意义以及它在概率论领域之外的应用。数学上的随机过程可以简单

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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。