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課程名稱 |
隨機過程與不確定性分析
Stochastic Processes and Uncertainty Analysis |
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開課學期 |
100-2 |
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授課對象 |
工學院 水利工程組 |
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授課教師 |
蔡宛珊 |
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課號 |
CIE7156 |
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課程識別碼 |
521EM7450 |
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班次 |
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學分 |
3 |
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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 |
星期三5(12:20~13:10)星期四2,3(9:10~11:10) |
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上課地點 |
土318B土研406 |
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備註 |
本課程以英語授課。
總人數上限：10人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002stochastic |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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 |
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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. |
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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 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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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) |
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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. |
Homework Assignments and Reports |
50% |
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2. |
Term Project and Presentation |
30% |
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3. |
Class Discussion and Participation |
20% |
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週次 |
日期 |
單元主題 |
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Week 1 |
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Introduction |
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Week 2 |
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Introduction to Real Analysis (1) |
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Week 3 |
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Introduction to Real Analysis (2) |
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Week 6 |
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Uncertainty Analysis (1) |
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Week 7 |
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Uncertainty Analysis (2) |
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Week 8 |
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Uncertainty Analysis (3) |
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Week 9 |
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Uncertainty Analysis (4) |
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Week 10 |
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Uncertainty Analysis Applciations |
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Week 11 |
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Uncertainty Analysis Applications |
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Week 12 |
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Stochastic Calculus (1) |
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Week 13 |
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Stochastic Calculus (2) |
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Week 14 |
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Stochastic Calculus (3) |
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Week 15 |
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Brownian motion and SPDE |
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Week 16 |
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Brownian motion and SPDE |
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Week 17 |
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Term Projet Presentations |
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Week 4-5 |
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Introduction to Real Analysis (3) |