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概率论导引（影印版）

样章
作者：
John B. Walsh
定价：
169.00元
ISBN：
978-7-04-063237-8
版面字数：
725.00千字
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：
2025-02-07
物料号：
63237-00
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：
概率论
暂无
  • 前辅文
  • Preface
  • Introduction
  • Chapter 1. Probability Spaces
    • §1.1. Sets and Sigma-Fields
    • §1.2. Elementary Properties of Probability Spaces
    • §1.3. The Intuition
    • §1.4. Conditional Probability
    • §1.5. Independence
    • §1.6. Counting: Permutations and Combinations
    • §1.7. The Gambler’s Ruin
  • Chapter 2. Random Variables
    • §2.1. Random Variables and Distributions
    • §2.2. Existence of Random Variables
    • §2.3. Independence of Random Variables
    • §2.4. Types of Distributions
    • §2.5. Expectations I: Discrete Random Variables
    • §2.6. Moments, Means and Variances
    • §2.7. Mean, Median, and Mode
    • §2.8. Special Discrete Distributions
  • Chapter 3. Expectations II: The General Case
    • §3.1. From Discrete to Continuous
    • §3.2. The Expectation as an Integral
    • §3.3. Some Moment Inequalities
    • §3.4. Convex Functions and Jensen’s Inequality
    • §3.5. Special Continuous Distributions
    • §3.6. Joint Distributions and Joint Densities
    • §3.7. Conditional Distributions, Densities, and Expectations
  • Chapter 4. Convergence
    • §4.1. Convergence of Random Variables
    • §4.2. Convergence Theorems for Expectations
    • §4.3. Applications
  • Chapter 5. Laws of Large Numbers
    • §5.1. The Weak and Strong Laws
    • §5.2. Normal Numbers
    • §5.3. Sequences of Random Variables: Existence*
    • §5.4. Sigma Fields as Information
    • §5.5. Another Look at Independence
    • §5.6. Zero-one Laws
  • Chapter 6. Convergence in Distribution and the CLT
    • §6.1. Characteristic Functions
    • §6.2. Convergence in Distribution
    • §6.3. Lévy’s Continuity Theorem
    • §6.4. The Central Limit Theorem
    • §6.5. Stable Laws*
  • Chapter 7. Markov Chains and Random Walks
    • §7.1. Stochastic Processes
    • §7.2. Markov Chains
    • §7.3. Classification of States
    • §7.4. Stopping Times
    • §7.5. The Strong Markov Property
    • §7.6. Recurrence and Transience
    • §7.7. Equilibrium and the Ergodic Theorem for Markov Chains
    • §7.8. Finite State Markov Chains
    • §7.9. Branching Processes
    • §7.10. The Poisson Process
    • §7.11. Birth and Death Processes*
  • Chapter 8. Conditional Expectations
    • §8.1. Conditional Expectations
    • §8.2. Elementary Properties
    • §8.3. Approximations and Projections
  • Chapter 9. Discrete-Parameter Martingales
    • §9.1. Martingales
    • §9.2. System Theorems
    • §9.3. Convergence
    • §9.4. Uniform Integrability
    • §9.5. Applications
    • §9.6. Financial Mathematics I: The Martingale Connection*
  • Chapter 10. Brownian Motion
    • §10.1. Standard Brownian Motion
    • §10.2. Stopping Times and the Strong Markov Property
    • §10.3. The Zero Set of Brownian Motion
    • §10.4. The Reflection Principle
    • §10.5. Recurrence and Hitting Properties
    • §10.6. Path Irregularity
    • §10.7. The Brownian Infinitesimal Generator*
    • §10.8. Related Processes
    • §10.9. Higher Dimensional Brownian Motion
    • §10.10. Financial Mathematics II: The Black-Scholes Model*
    • §10.11. Skorokhod Embedding*
    • §10.12. Lévy’s Construction of Brownian Motion*
    • §10.13. The Ornstein-Uhlenbeck Process*
    • §10.14. White Noise and the Wiener Integral*
    • §10.15. Physical Brownian Motion*
    • §10.16. What Brownian Motion Really Does
  • Bibliography
  • Index

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