隨機過程
Stochastic Processes
| 節 | 週四 | 週五 |
|---|---|---|
2 09:00–09:50 | 隨機過程 SA223 | |
5 13:20–14:10 | 隨機過程 SA223 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
Syllabus: Chapter 1 Review of Probability 1.1 Probability Spaces 1.2 Conditional Probability and Independence 1.3 Random Variables, Distributions and Independence 1.4 Expectation, Variance and Covariance 1.5 Some Simple Inequalities 1.6 Applications of the Linearity of Expectation Chapter 2 Second Moment Calculations 2.1 Some Elementary Inequalities 2.2 Convergence in Probability 2.3 Classical Law of Large Numbers 2.4 Bernstein Polynomials 2.5 Cliques in the Erdos-Renyi Random Graph Chapter 3 Exponential Inequalities 3.1 Hoeffding Inequality 3.2 Johnson-Linderstrauss Lemma 3.3 Hoeffding-Chernoff Inequality 3.4 Azuma Inequality 3.5 Applications of Azuma Inequality Chapter 4 Finite State Markov Chains 4.1 Definitions and Basic Properties 4.2 Stationary Distributions 4.3 Convergence Theorem 4.4 Reversible Markov Chains Chapter 5 Countable Markov Chains 5.1 Recurrence and Transience 5.2 Positive Recurrence and Null Recurrence 5.3 Branching Process Chapter 6 Continuous-Time Markov Chains 6.1 Poisson Process* 6.2 Finite State Space 6.3 Birth-and Death Processes 6.4 General Case
Prerequisite: undergraduate probability, linear algebra, advanced calculus
Exams: Quiz I(90 points): March 14, Friday, 09:00~10:00 Midterm Exam (180 points): April 11, 13:20~15:20 Quiz II (90 points): May 9, 09:00~10:00 Final (180 points): June 6, 13:20~15:20, Grading: (90+180+90+180)/5
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Textbooks: 1. Introduction to Probability by Dmitry Panchenko 2. Introduction to Stochastic Processes by Gregory F.Lawler 3. Foundations of Data Science by Avrim Blum, John Hopcroft and Ravindran Kannan (optional)