概率论和随机过程 : 第2版

概率论和随机过程 : 第2版

(美) 凯罗勒夫, 著

出版社:世界图书出版公司北京公司

年代:2012

定价:45.0

书籍简介:

本书是以作者在Princeton大学和Maryland大学的讲义为蓝本扩充而成,书中的内容正好可作为《概率论和随机过程》课程一学年的独立教材。这对于高年级的本科生、研究生和想要了解本科目基础知识的科研人员都是相当有用的。

书籍目录:

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

内容摘要:

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).

书籍规格:

书籍详细信息
书名概率论和随机过程 : 第2版站内查询相似图书
9787510044106
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出版地北京出版单位世界图书出版公司北京公司
版次影印本印次1
定价(元)45.0语种英文
尺寸21 × 17装帧平装
页数 372 印数

书籍信息归属:

概率论和随机过程 : 第2版是世界图书出版公司北京公司于2012.3出版的中图分类号为 O21 的主题关于 概率论-高等学校-教材-英文 ,随机过程-高等学校-教材-英文 的书籍。