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
97-2 
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
全/半年
半年 
必/選修
選修 
上課時間
星期一6,7,8(13:20~16:20) 
上課地點
土224 
備註
本課程以英語授課。建議先修課程:統計學或工程統計,微積分或工程數學(一),或經授課教師同意。
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/972stochastic 
課程簡介影片
 
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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
THE OVERALL OBJECTIVE OF THIS COURSE IS TO FAMILIARIZE STUDENTS WITH BASIC CONCEPTS OF MATHEMATICAL MODELING UNDER UNCERTAINTY. STUDENTS ARE EXPECTED TO GAIN A BASIC UNDERSTANDING OF STOCHASTIC PROCESSES, UNCERTAINTY ANALYSIS AND FUNDAMENTAL STOCHASTIC CALCULUS USEFUL FOR STOCHASTIC MODELING. THIS COURSE WILL PROVIDE STUDENTS WITH FUNDAMENTAL KNOWLEDGE AND QUANTITATIVE APPROACHES NECESSARY FOR MODELING NATURAL PROCESSES UNDER UNCERTAINTY. THIS COURSE WILL BE TAUGHT IN ENGLISH. 
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
 
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) 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework Assignments and Reports 
50% 
 
2. 
Term Project and Presentation 
30% 
 
3. 
Class Discussion and Participation 
20% 
 
 
課程進度
週次
日期
單元主題
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