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機 率 論 授課教師：黃炎坤

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機 率 論

授課教師：黃炎坤 (分機 65137)

Probability Theory (1)

1、Measure-Theoretic preliminaries (1) Basic definitions

(2) Random variables (3) Expected value (4) Independence 2、Laws of Large Numbers

(1) Weak laws of large numbers (2) Borel-Cantelli Lemmas (3) Zero-One Laws

(4) The Strong law of large numbers (5) Law of the Iterated Logarithm (6) Convergence of random series 3、Central Limit Theorems

(1) The DeMoivre Laplace Theorem (2) Weak convergence

(3) Characteristic functions

1. Definition, inversion formula 2. Weak convergence

3. Moments and derivatives (4) The Lindeberg-Feller Theorem 4、Random walks

(1) Stopping times (2) Recurrence, Transient

Reference ：

1、Kai Lai Chung：A Course in Probability Theory 2、Yuan Shih Chow & Henry Teicher：Probability Theory

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