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概率论（影印版）

样章
作者：
Daniel W. Stroock
定价：
135.00元
ISBN：
978-7-04-059302-0
版面字数：
500.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2023-03-24
物料号：
59302-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数理统计学
暂无
  • 前辅文
  • Chapter 1. Some Background and Preliminaries
    • 1.1 The Language of Probability Theory
      • 1.1.1. Sample Spaces and Events
      • 1.1.2. Probability Measures
    • Exercises for 1.1
    • 1.2 Finite and Countable Sample Spaces
      • 1.2.1. Probability Theory on a Countable Space
      • 1.2.2. Uniform Probabilities and Coin Tossing
      • 1.2.3. Tournaments
      • 1.2.4. Symmetric Random Walk
      • 1.2.5. De Moivre’s Central Limit Theorem
      • 1.2.6. Independent Events
      • 1.2.7. The Arc Sine Law
      • 1.2.8. Conditional Probability
    • Exercises for 1.2
    • 1.3 Some Non-Uniform Probability Measures
      • 1.3.1. Random Variables and Their Distributions
      • 1.3.2. Biased Coins
      • 1.3.3. Recurrence and Transience of Random Walks
    • Exercises for 1.3
    • 1.4 Expectation Values
      • 1.4.1. Some Elementary Examples
      • 1.4.2. Independence and Moment Generating Functions
      • 1.4.3. Basic Convergence Results
    • Exercises for 1.4
    • Comments on Chapter 1
  • Chapter 2. Probability Theory on Uncountable Sample Spaces
    • 2.1 A Little Measure Theory
      • 2.1.1. Sigma Algebras, Measurable Functions, and Measures
      • 2.1.2. Π- and Λ-Systems
    • Exercises for 2.1
    • 2.2 A Construction of Pp on {0, 1}Z+
      • 2.2.1. The Metric Space {0, 1}Z+
      • 2.2.2. The Construction
    • Exercises for 2.2
    • 2.3 Other Probability Measures
      • 2.3.1. The Uniform Probability Measure on [0, 1]
      • 2.3.2. Lebesgue Measure on R
      • 2.3.3. Distribution Functions and Probability Measures
    • Exercises for 2.3
    • 2.4 Lebesgue Integration
      • 2.4.1. Integration of Functions
      • 2.4.2. Some Properties of the Lebesgue Integral
      • 2.4.3. Basic Convergence Theorems
      • 2.4.4. Inequalities
      • 2.4.5. Fubini’s Theorem
    • Exercises for 2.4
    • 2.5 Lebesgue Measure on RN
      • 2.5.1. Polar Coordinates
      • 2.5.2. Gaussian Computations and Stirling’s Formula
    • Exercises for 2.5
    • Comments on Chapter 2
  • Chapter 3. Some Applications to Probability Theory
    • 3.1 Independence and Conditioning
      • 3.1.1. Independent σ-Algebras
      • 3.1.2. Independent Random Variables
      • 3.1.3. Conditioning
      • 3.1.4. Some Properties of Conditional Expectations
    • Exercises for 3.1
    • 3.2 Distributions that Admit a Density
      • 3.2.1. Densities
      • 3.2.2. Densities and Conditioning
    • Exercises for 3.2
    • 3.3 Summing Independent Random Variables
      • 3.3.1. Convolution of Distributions
      • 3.3.2. Some Important Examples
      • 3.3.3. Kolmogorov’s Inequality and the Strong Law
    • Exercises for 3.3
    • Comments on Chapter 3
  • Chapter 4. The Central Limit Theorem and Gaussian Distributions
    • 4.1 The Central Limit Theorem
      • 4.1.1. Lindeberg’s Theorem
    • Exercises for 4.1
    • 4.2 Families of Normal Random Variables
      • 4.2.1. Multidimensional Gaussian Distributions
      • 4.2.2. Standard Normal Random Variables
      • 4.2.3. More General Normal Random Variables
      • 4.2.4. A Concentration Property of Gaussian Distributions
      • 4.2.5. Linear Transformations of Normal Random Variables
      • 4.2.6. Gaussian Families
    • Exercises for 4.2
    • Comments on Chapter 4
  • Chapter 5. Discrete Parameter Stochastic Processes
    • 5.1 Random Walks Revisited
      • 5.1.1. Immediate Rewards
      • 5.1.2. Computations via Conditioning
    • Exercises for 5.1
    • 5.2 Processes with the Markov Property
      • 5.2.1. Sequences of Dependent Random Variables
      • 5.2.2. Markov Chains
      • 5.2.3. Long-Time Behavior
      • 5.2.4. An Extension
    • Exercises for 5.2
    • 5.3 Markov Chains on a Countable State Space
      • 5.3.1. The Markov Property
      • 5.3.2. Return Times and the Renewal Equation
      • 5.3.3. A Little Ergodic Theory
    • Exercises for 5.3
    • Comments on Chapter 5
  • Chapter 6. Some Continuous-Time Processes
    • 6.1 Transition Probability Functions and Markov Processes
      • 6.1.1. Transition Probability Functions
    • Exercises for 6.1
    • 6.2 Markov Chains Run with a Poisson Clock
      • 6.2.1. The Simple Poisson Process
      • 6.2.2. A Generalization
      • 6.2.3. Stationary Measures
    • Exercises for 6.2
    • 6.3 Brownian Motion
      • 6.3.1. Some Preliminaries
      • 6.3.2. L´evy’s Construction
      • 6.3.3. Some Elementary Properties of Brownian Motion
      • 6.3.4. Path Properties
      • 6.3.5. The Ornstein–Uhlenbeck Process
    • Exercises for 6.3
    • Comments on Chapter 6
  • Chapter 7. Martingales
    • 7.1 Discrete Parameter Martingales
      • 7.1.1. Doob’s Inequality
    • Exercises for 7.1
    • 7.2 The Martingale Convergence Theorem
      • 7.2.1. The Convergence Theorem
      • 7.2.2. Application to the Radon–Nikodym Theorem
    • Exercises for 7.2
    • 7.3 Stopping Times
      • 7.3.1. Stopping Time Theorems
      • 7.3.2. Reversed Martingales
      • 7.3.3. Exchangeable Sequences
    • Exercises for 7.3
    • 7.4 Continuous Parameter Martingales
      • 7.4.1. Progressively Measurable Functions
      • 7.4.2. Martingales and Submartingales
      • 7.4.3. Stopping Times Again
      • 7.4.4. Continuous Martingales and Brownian Motion
      • 7.4.5. Brownian Motion and Differential Equations
    • Exercises for 7.4
    • Comments on Chapter 7
  • Notation
  • Bibliography
  • Index

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