隨機過程
Stochastic Processes
| 節 | 週三 | 週四 |
|---|---|---|
3 10:10–11:00 | 隨機過程 SA213（光復） 2 節連堂 | |
4 11:10–12:00 | ||
8 16:30–17:20 | 隨機過程 SA213（光復） |
* 根據陽明交大上課時間表所列
Stochastic processes will broadly appear in a part of science, finance and social studies. The aim of this course is to understand stochastic process from the theoretical point of view and be familiar with how to handle it at the basic level. The course will be considered as an application of Probability Theory and Advanced Probability Theory. Thus we assume that students have been already familiar with measure-theory based probability theory.
Lebesgue Integral, Measure Theory, Probability Theory, and Advanced Probability Theory are required.
無備註
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We will have report(s) and exam for evaluation.
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction to Stochastic Processes & Review of Probability Theory |
| 第 2 週 | Review of Probability Theory |
| 第 3 週 | Discrete Time Stochastic Processes |
| 第 4 週 | Martingales: Random Walks |
| 第 5 週 | Martingales: Convergence Theorem |
| 第 6 週 | Markov Processes |
| 第 7 週 | Markov Chains: Recurrence and Transience |
| 第 8 週 | Markov Chains: Irreducibility and Invariant distribution |
| 第 9 週 | Continuous Stochastic Processes |
| 第 10 週 | Continuous Stochastic Processes |
| 第 11 週 | Brownian Motion |
| 第 12 週 | Brownian Motion |
| 第 13 週 | Brownian Motion |
| 第 14 週 | Examination |
| 第 15 週 | Backup |
| 第 16 週 | Backup |
We will have lecture note for each section of the course. To more knowledge or details, we will show some references below. -[Basic] R. Bass, (2012). Stochastic Processes, Cambridge University Press. -[Basic] R. Durrett, (2012). Essentials of Stochastic Processes, Springer. -[in Japanese] Y. Higuchi, and M. Nishio, (2006). Kakuritsukatei Nyumon, Baihu-kan. -[in Japanese] K. Ito, (2007). Kakuritsuron no Kiso [New edition], Iwanami-Shoten. -[Mathematical Finance] I. Karatzas, and S. E. Shreve, (2014). Brownian Motion and Stochastic Calculus, Springer. -[Basic] G. F. Lawler, (2018). Introduction to Stochastic Processes, Chapman and Hall/CRC. -[Advanced] T. M. Liggett, (1985). Interacting Particle Systems, Springer. -[Basic] D. W. Stroock, (2005). An Introduction to Markov Processes, Springer. -[Random walk theory] W. Woess, (2000). Random Walks on Infinite Graphs and Groups, Cambridge University Press.
- 地點
- SA239
- 時間
- TBA
- 聯絡方式
- Make an appointment by email: y.chino@math.nctu.edu.tw