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課程名稱 |
隨機過程導論
Introduction to Stochastic Processes |
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開課學期 |
107-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
黃建豪 |
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課號 |
MATH5504 |
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課程識別碼 |
221 U4410 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三6,7(13:20~15:10)星期四3(10:20~11:10) |
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上課地點 |
天數302天數302 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071MATH5504_h |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
Stochastic processes have various applications in science, biology, engineering, social science. This course is for 3+ year under students and graduates. Students with disciplines other than math are welcome, but be ready to write a lot of proofs. The course intends to cover basic measure theory. Students with background in measure theory may have to present selected materials. For example, 2007 Resnick Ch5 Poisson processes as random measure. More info on my course page https://sites.google.com/site/chienhaouci08/math_2a/introsp |
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課程目標 |
Markov chain, Poisson process, Measure theory, Martingales, Renewal theory, Brownian motion |
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課程要求 |
Elementary probability, basic linear algebra and basic analysis. |
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預期每週課後學習時數 |
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Office Hours |
每週一 13:00~14:00
每週四 15:30~16:30 |
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指定閱讀 |
R. Durrett 2016 Essentials of stochastic processes 3rd (ebook can be downloaded from NTU Library) Ch 125
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參考書目 |
Grinstead and Snell 2006 Introduction to probability 2nd Ch 11
G. Lawler 2006 Introduction to stochastic processes 2nd Ch1,2,5
T. Tao 2011 An introduction to measure theory Ch1 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm1 |
30% |
Week 8 10/31 tentative |
2. |
Midterm2 |
30% |
Week 15 12/19 tentative |
3. |
Homework |
30% |
每周繳交or上台演習 |
4. |
Class participation |
10% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/12,9/13 |
Review for probability;
finite state Markov Chain absorbing |
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第2週 |
9/19,9/20 |
finite state Markov Chain regular ergodic;
passage times |
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第3週 |
9/26,9/27 |
Lawler 1.4 return time, spectral analysis, Dur 1.3 stopping time, Strong Markov property, transience and recurrence;
Dur 1.3 |
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第4週 |
10/03,10/04 |
Dur 1.3, 1.6; Lawler 1.5, 1.6;
Poisson processes |
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第5週 |
10/10,10/11 |
10/10 Holiday;
PP |
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第6週 |
10/17,10/18 |
Durrett 2.1-2.4;
Dur 1.11 Countable Markov Chain/RW Lawler Ch2; |
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第7週 |
10/24,10/25 |
Short review; Dur 1.5.1 reversible;
1.5.2 |
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第8週 |
10/31,11/01 |
Midterm 1 Week 1-6;
Measure theory1 |
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第9週 |
11/07,11/08 |
Measure theory23;
4 |
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第10週 |
11/14,11/15 |
Self-study;11/15 Holiday |
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第11週 |
11/21,11/22 |
Oral/Measure theory5 |
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第12週 |
11/28,11/29 |
Measure theory 67;
linear operator |
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第13週 |
12/05,12/06 |
Royden 3rd 5.2 BV/ 5.4 AC;
Dur 5.1 Martingales |
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第14週 |
12/12,12/13 |
Dur 5.2-3;
5.4.2 |
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第15週 |
12/19,12/20 |
Midterm 2 Week Measure theory and martingale;
Oral |
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第16週 |
12/26,12/27 |
Durrett 3.1 Renewal |
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第17週 |
1/02,1/03 |
Brownian motions |
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