- 概率论(第2版)(英文版)
- - 作者：A.N.Shiryaev|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787506271882
  - 出版日期：2004/08/01
  - 页数：621
- 售价：39.6

内容大纲
    本书是一部经典的概率论研究生教材。本书的俄文原版于1979年出版，作者在莫斯科大学曾以本书内容为蓝本，为概率论研究生讲课多年，教学效果很好。1984年Springer出版了该书的英文版，本书是该英文版的第2版，本版内容比第1版增加了30余页。
    目次：初等概率论；概率论的数学基础；概率测度的收敛性及中心极限定理；独立随机变量的序列与加项；平稳随机序列及遍历性理论；平稳随机序列及L2理论；形成鞅的随机变量序列；形成马尔可夫链的随机变量序列。
    读者对象：数学专业的研究生。
作者介绍
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 o-algebras. Measurable Spaces
  §3.Methods of Introducing Probability Measures on Measurable Spaces
  §4.Random Variables. Ⅰ.
  §5.Random Elements
  §6.Lebesgue Integral.Expectation
  §7.Conditional Probabilities and Conditional Expectations with Respect to a o-Algebra
  §8.Random Variables. Ⅱ.
  §9.Construction of a Process with Given Finite-Dimensional Distribution
  §10.Various Kinds of Convergence of Sequences of Random Variables
  §11.The Hilbert Space of Random Variables with Finite Second Moment
  §12.Characteristic Functions
  §13.Gaussian Systems
CHAPTER Ⅲ  Convergence of Probability Measures.Central Limit Theorem
  §1.Weak Convergence of Probability Measures and Distributions
  §2.Relative Compactness and Tightness of Families of Probability Distributions
  §3.Proofs of Limit Theorems by the Method of Characteristic Functions
  §4.Central Limit Theorem for Sums of Independent Random Variables. Ⅰ. The Lindeberg Condition
  §5.Central Limit Theorem for Sums of Independent Random Variables. Ⅱ. Nonclassical Conditions
  §6.Infinitely Divisible and Stable Distributions
  §7.Metrizability of Weak Convergence
  §8.On the Connection of Weak Convergence of Measures with Almost Sure Convergence of Random Elements ("Method of a Single Probability Space")
  §9.The Distance in Variation between Probability Measures. Kakutani-Hellinger Distance and Hellinger Integrals. Application to Absolute Continuity and Singularity of Measures
  §10.Contiguity and Entire Asymptotic Separation of Probability Measures
  §11.Rapidity of Convergence in the Central Limit Theorem
  §12.Rapidity of Convergence in Poisson's Theorem
CHAPTER Ⅳ  Sequences and Sums of Independent Random Variables
  §1.Zero-or-One Laws
  §2.Convergence of Series
  §3.Strong Law of Large Numbers
  §4.Law of the Iterated Logarithm
  §5.Rapidity of Convergence in the Strong Law of Large Numbers and in the Probabilities of Large Deviations
CHAPTER Ⅴ  Stationary (Strict Sense) Random Sequences and Ergodic Theory

  §1.Stationary (Strict Sense) Random Sequences.Measure-Preserving Transformations
  §2.Ergodicity and Mixing
  §3.Ergodic Theorems
CHAPTER Ⅵ  Stationary (Wide Sense) Random Sequences. L2 Theory
  §1.Spectral Representation of the Covariance Function
  §2.Orthogonal Stochastic Measures and Stochastic Integrals
  §3.Spectral Representation of Stationary (Wide Sense) Sequences
  §4.Statistical Estimation of the Covariance Function and the Spectral Density
  §5.Wold's Expansion
  §6.Extrapolation, Interpolation and Filtering
  §7.The Kalman-Bucy Filter and Its Generalizations
CHAPTER Ⅶ  Sequences of Random Variables that Form Martingales
  §1.Definitions of Martingales and Related Concepts
  §2.Preservation of the Martingale Property Under Time Change at a Random Time
  §3.Fundamental Inequalities
  §4.General Theorems on the Convergence of Submartingales and Martingales
  §5.Sets of Convergence of Submartingales and Martingales
  §6.Absolute Continuity and Singularity of Probability Distributions
  §7.Asymptotics of the Probability of the Outcome of a Random Walk with Curvilinear Boundary
  §8.Central Limit Theorem for Sums of Dependent Random Variables
  §9.Discrete Version of Ito's Formula
  §10.Applications to Calculations of the Probability of Ruin in Insurance
CHAPTER Ⅷ  Sequences of Random Variables that Form Markov Chains
  §1.Definitions and Basic Properties
  §2.Classification of the States of a Markov Chain in Terms of Arithmetic Properties of the Transition Probabilities p(n)ij
  §3.Classification of the States of a Markov Chain in Terms of Asymptotic Properties of the Probabilities p(n)ii
  §4.On the Existence of Limits and of Stationary Distributions
  §5.Examples
Historical and Bibliographical Notes
References
Index of Symbols
Index

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