这本书以悠闲的方式涵盖了一个完整学年概率课程的所有标准内容，重点是在研究生或高年级本科生高级课程中的金融分析应用。它融入了相当多的测度论和实分析，但以特别简单和直观的方式介绍了σ-域、测度论和期望。每章都包含大量的例子和练习，丰富了教材的呈现。 Walsh是这个学科的一位大师，他写了一本关于概率的精彩书籍，恰好适合这个水平。他以悠闲的步调覆盖了学生需要了解的所有重要主题，并提供了优秀的例子。我很遗憾，几年前我教授这门课程时，他的书还没有问世。 —Ioannis Karatzas, Columbia University 在这本精彩的书中，John Walsh呈现了概率论的全景图，从关于均值、中位数和众数的基本事实开始，继而对马尔可夫链和鞅进行了优秀的描述，并以布朗运动为高潮。作者的个人风格贯穿全书；他成功地将严谨性与对关键思想的强调结合起来，使读者在被太多细节围绕时也不会忘记森林的全貌。正如前言所述，“要愉快地教授一门课程，同时也应该在学习过程中获得乐趣。”事实上，几乎所有的教师都将从这本书中学到一些新知识（例如，Skorokhod嵌入的潜在理论证明），同时它对学生来说既有吸引力又易于理解。 —Yuval Peres, Microsoft

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