概率论

出版时间：2004-11  出版社：北京世图  作者：A.N.Shiryaev  页数：621  
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内容概要

In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probability, Statistics, and Stochastic Processors, I, II" and published by that University. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a threesemester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space. In this connection, we stated in the Preface to the first edition that only probability theory and the theory of random processes with discrete time were really adequately presented.

作者简介

作者:( )A.N.Shiryaev[

书籍目录

Preface to the Second Edition Preface to the First Edition Introduction CHAPTER I Elementary Probability Theory   1. Probabilistic Model of an Experiment with a Finite Number of Outcomes   2. Some Classical Models and Distributions   3. Conditional Probability. Independence   4. Random Variables and Their Properties   5. The Bernoulli Scheme. I. The Law of Large Numbers   6. The Bernoulli Scheme. II. Limit Theorems (Local， De Moivre-Laplace， Poisson)   7. Estimating the Probability of Success in the Bernoulli Scheme   8. Conditional Probabilities and Mathematical Expectations with Respect to Decompositions   9. Random Walk. I. Probabilities of Ruin and Mean Duration in Coin Tossing   10. Random Walk. II. Reflection Principle. Arcsine Law   11. Martingales. Some Applications to the Random Walk   12. Markov Chains. Ergodic Theorem. Strong Markov Property CHAPTER II Mathematical Foundations of Probability Theory   1. Probabilistic Model for an Experiment with Infinitely Many Outcomes. Kolmogorov‘s Axioms   2. Algebras and a-algebras. Measurable Spaces   3. Methods of Introducing Probability Measures on Measurable Spaces   ……CHAPTER III Conergence of Probability Measures.Central Limit TheoremCHAPTER IV  Sequences and Sums of Independent Random VariablesCHAPTER V Stationary(Stircty Sense)Random Sequences and Ergodic TheoryCHAPTER VI Stationary(Wide Sense)Random Sequences L2 TheoryCHAPTER VII Sequences of Random Variables that Form MartingalseCHAPTER VIII Sequences of Random Variables that Form Markov ChainsHistorical and Bibographical NotesReferncesIndex of SymbolsIndex

用户评论 (总计16条)

•   本书是俄文翻译成英文的，所以英文有点怪怪的，但是理解没问题的
  书的一开始几章是比较基本的概率论，和我们高中开始一直到大学的都很类似，但是系统的多，符号用的稍微有点不适应，多看看吧。
  后面就是现代的精华了，还没看到，感觉章节安排的不错
  这本书估计上课要一年制的，阅读量有点大，自己看估计也要个1-2月才行
•   帮老师买的，自己没有看过，想着应该不多的。
•   正好我放假回家了，书也到家了，很及时。就是用快递能送到村里就好了。
•   老师推荐的教材，正在使用中
•   相对于国内大学出版的教材，本书在体系上还是很全的。不过不适合初学者，基础部分相对过少。总之还是本难得的好书
•   不要以为基础数学就不需要学概率论了，有了广博的知识储蓄才能厚积薄发，此书内容也是很深厚，先来古典的概率论，再来现在概率论，就是引用了测度为工具的，学习此书以前学了本科的概率论和实变函数会较容易学懂！
•   这本书原来是俄文的，其实也有中文版的。这本英文的似乎并不一定有中文翻译的好。书的作者不用说了，是科尔模格罗夫的学生，是随机过程方面的老权威。书的结构很好，第一章讲了一些直观上的概率论，第二章讲了公理概率论，后面涉及到了martingale和随机过程。深度一般，但是非常浅显，的确是一本好的教科书。
•   作者是Kolmogrov的学生，此书内容涵盖较广，较Durret略难读。作者的另一本 随机金融概要 多处引用，可作为常用参考书。
•   是一本概率方面全面的好书。
•   fhdddddddddddh
•   不错的书，但是发货实在太慢了！！！！
•   书是好书，就是印刷太差了，影响阅读！感觉就是80年代前的
•   好书 测度讲的很清楚 就是习题少 不过适合我这种快速阅读的人
•   内容很基本，对于基本概念的论述和基本方法讲解的都很透彻。
•   有几页是模糊的，书内容是ok的
•   经典教材，看不了俄文就看英译本，中译本太次。。