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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] 电子书 下载 mobi epub pdf txt

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研究随机过程的方法多种多样，主要可以分为两大类：一类是概率方法，其中用到轨道性质、停时和随机微分方程等；另一类是分析的方法，其中用到测度论、微分方程、半群理论、函数堆和希尔伯特空间等。实际研究中常常两种方法并用。另外组合方法和代数方法在某些特殊随机过程的研究中也有一定作用。研究的主要内容有：多指标随机过程、无穷质点与马尔可夫过程、概率

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