課程資訊
課程名稱
隨機過程與不確定性分析
Stochastic Processes and Uncertainty Analysis 
開課學期
105-2 
授課對象
工學院  水利工程組  
授課教師
蔡宛珊 
課號
CIE7156 
課程識別碼
521EM7450 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期四3,4,6(10:20~14:10) 
上課地點
土研405 
備註
本課程以英語授課。
限本系所學生(含輔系、雙修生)
總人數上限:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1052CIE7156_ 
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課程概述

PRELIMINARIES
FUNDAMENTALS OF REAL VARIABLES
MATHEMATICAL PRELIMINARIES
FUNDAMENTALS OF UNCERTAINTY ANALYSIS
FUNDAMENTALS OF RANDOM PROCESSES

MARTINGALES, STOPPING TIMES AND FILTRATIONS
STOCHASTIC PROCESSES AND SIGMA FIELDS
STOPPING TIMES
CONTINUOUS TIME MARTINGALES
REYNOLDS TRANSPORT THEOREM
CONSERVATION OF DISSOLVED CONSTITUENT MASS

BROWNIAN MOTION
BROWNIAN MOTION
MARKOV PROPERTY
THE BROWNIAN SAMPLE PATHS

STOCHASTIC INTEGRATION
CONSTRUCTION OF THE STOCHASTIC INTEGRAL
THE CHANGE-OF-VARIABLE FORMULA
GENERALIZED ITO RULE FOR BROWNIAN MOTION

STOCHASTIC DIFFERENTIAL EQUATIONS (IF TIME PERMITTED)
STRONG SOLUTIONS
WEAK SOLUTIONS
APPROXIMATION METHODS FOR UNCERTAINTY ANALYSIS
FIRS-ORDER VARIANCE ESTIMATION METHOD
ROSENBLUETH;S PROBABILISTIC POINT ESTIMATE METHOD
HARR’S PROBABILISTIC POINT ESTIMATE METHOD
LI’S PROBABILISTIC POINT ESTIMATE METHOD
 

課程目標
待補 
課程要求
先修課程: 統計學或工程統計, 微積分或工程數學(一),或授課教師同意 
預期每週課後學習時數
 
Office Hours
 
指定閱讀
 
參考書目
1. “INTRODUCTION TO PROBABILITY MODELS” BY SHELDON ROSS, 9TH ED., ACADEMIC PRESS (2006)
2. “BROWNIAN MOTION AND STOCHASTIC CALCULUS” BY KARATZAS AND SHREVE, SPRINGER (1991) [ISBN 0-387-97655-8]
3. “HYDROSYSTEMS ENGINEERING UNCERTAINTY ANALYSIS” BY TUNG AND YEN, MCGRAW-HILL (2005) [ISBN 0-07-145159-5]
4. “THE ESSENTIALS OF REAL VARIABLES” BY RESEARCH AND EDUCATION ASSOCIATION (1994)
 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
Week 1
2/23  make up class 
Week 2
3/02  make up class 
Week 3
3/09  make up class 
Week 4
3/16  Introduction 
Week 5
3/23  Probability
(from Handbook of Stochastic Methods by Gardiner 2004)
Reading Assignment: Chapter 1.1-1.3 
Week 6
3/30  Markov Process

Reading Assignment 2.6-2.7 
Week 9
4/20  Make-up class on 5/1 10-12am 
Week 10
4/27  Mak-up class on 5/7 10-12am 
Week 16
6/08  make-up class 6/5 10-12 
Week 17
6/15  make-up class 6/12 10-12