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概率论导引（影印版）

样章
作者：
John B. Walsh
定价：
169.00 元
版面字数：
725千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2025年
ISBN：
978-7-04-063237-8
物料号：
63237-00
出版时间：
2025-02-07
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
  • 目录
    • 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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