高等概率论¶

23Fall DATA620019，现代概率论基础I，张静茹

使用测度工具的概率论。

主要内容¶

• Measure Theory
  1. Probability Spaces
  2. Distributions
  3. Random Variables
  4. Integration
  5. Properties of the Integral
  6. Expected Value
  7. Product Measures, Fubini's Theorem
• Laws of Large Numbers
  1. Independence
  2. Weak Laws of Large Numbers
  3. Borel-Cantelli Lemmas
  4. Strong Law of Large Numbers
  5. Convergence of Random Series*
• Central Limit Theorems
  1. The De Moivre-Laplace Theorem
  2. Weak Convergence
  3. Characteristic Functions
  4. Central Limit Theorems
  5. Local Limit Theorems*
  6. Poisson Convergence
  7. Poisson Processes
• Martingales
  1. Conditional Expectation

参考书¶

Probability: Theory and Examples 5ed, Rick Durrett

体会¶

好多定理。