图书信息
图书目录
概率论导引（影印版）
暂无简介
作者：
John B. Walsh
定价：
169.00元
出版时间：
2025-02-07
ISBN：
978-7-04-063237-8
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
重点项目：
暂无
版面字数：
725.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
