課程資訊
課程名稱
 連續時間隨機過程
Continuous-Time Stochastic Processes 
開課學期
 109-2 
授課對象
 理學院  數學研究所  
授課教師
 黃建豪 
課號
 MATH5254 
課程識別碼
 221 U8930 
班次
  
學分
 3.0 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期四2,3,4(9:10~12:10) 
上課地點
 天數304 
備註
 總人數上限：40人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1092MATH5254_h 
課程簡介影片
 
核心能力關聯
 本課程尚未建立核心能力關連
課程大綱
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課程概述

Basic concepts for continuous-time stochastic processes, Poisson point processes and Gaussian processes. Spectral analysis of stationary processes. Renewal theory. Continuous-time Markov processes. Interacting particle systems. Examples from many fields of sciences.
Martingale theory and stochastic calculus will NOT be covered, 他們在機率論二.  

課程目標
 We will discuss various types of stochastic processes and mathematical tools for understanding the random phenomenon which depends on time continuously. Providing scientific examples for students to get used to real applications. Systems with continuous parameters are benchmarks for discrete problems. Poisson and Gaussian distributions are two typical cases when experts do stochastic modeling. Renewal theory is the tool for analyzing systems repeating itself again and again. The interacting particle system, especially the contact process, is a way probabilists understanding the infectious virus. 
課程要求
 Basic measure theory, say Royden Ch 1-6 
預期每週課後學習時數
  
Office Hours
 每週三 12:30~13:30 
指定閱讀
 https://en.wikipedia.org/wiki/Stochastic_process#Definitions
Bremaud, Fourier Analysis and Stochastic Processes (2014) NTU Lib
Resnick, Adventures in Stochastic Processes (1992)
Liggett, Interacting Particle Systems (1985)
Daley and Vere-Jones, An introduction to the theory of point processes (2003) NTU Lib
Time series, Biology, Risk, ... 
參考書目
 依主題輪流上台報告, 做習題.
Martingale theory and stochastic calculus will NOT be covered, 他們在機率論二.
I Basics: Lecturer
II Stationary: https://en.wikipedia.org/wiki/Stationary_process
Ref: Bremaud Ch 3
III-1 CTMC, generator: https://en.wikipedia.org/wiki/Continuous-time_Markov_chain
Ref: Resnick Ch 5
III-2 Interacting particle systems
https://en.wikipedia.org/wiki/Contact_process_(mathematics)
https://en.wikipedia.org/wiki/Voter_model
https://en.wikipedia.org/wiki/Asymmetric_simple_exclusion_process
Ref: Liggett
III-3 Diffusion: Bessel processes
IV Point processes: https://en.wikipedia.org/wiki/Point_process
Ref: Resnick Ch 4
V Renewals: (May not have time)
Ref: Resnick Ch 3
See also images, simulations, examples from WWW 
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/25  10:20-12:10 Measure-theoretic Probability, Stochastic Processes;
1 hr video: Functional analysis 
第2週
 3/04  10:20-12:10 Poisson point processes
1 hr video: Hilbert spaces 
第3週
 3/11  Gaussian processes 
第4週
 3/18  報告, 習題課 Stationary processes: Continuity of paths 
第5週
 3/25  Stationary processes 
第6週
 4/01  Spring break 
第7週
 4/08  Spectral analysis of stationary processes 
第8週
 4/15  Applications 
第9週
 4/22  CTMC and Semigroup 
第10週
 4/29  自主 2 hours + 1 hour video 
第11週
 5/06  Diffusion and applications 
第12週
 5/13  IPS and Contact processes 
第13週
 5/20  Voter model and Exclusion processes 
第14週
 5/27  Point processes 
第15週
 6/03  Point processes 
第16週
 6/10  Applications 
第17週
 6/17  Special processes