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課程名稱 |
隨機過程
Stochastic Processes |
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開課學期 |
103-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
諾 曼 |
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課號 |
MATH5501 |
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課程識別碼 |
221 U5510 |
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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 |
星期二4(11:20~12:10)星期四3,4(10:20~12:10) |
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上課地點 |
天數305天數305 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032MATH5501 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
Markov chains, branching processes, Brownian motion, introduction to stochastic
integration and Ito's formula.
Time permitting: additional material on these or other topics (to discus). |
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課程目標 |
This course is an introduction to Stochastic Processes aimed at students with a solid
knowledge of basic Probability theory. Stochastic processes (that is, systems evolving randomly in time),
are the basic objects used in a wide variety of applications, such as Finance, Statistics, Physics, Telecom,
etc. We will cover the standard examples of Markov chains, Branching Processes and Brownian Motion,
with an introduction to stochastic calculus and its applications (in particular in Finance). The precise
direction of the course will be discussed with the students, to choose the topics studied, the balance between
theory and practice, and the type of activities in class. In particular, half of the final grade will consist of
projects in groups (or not), to see the new tools in action. These projects can be: study reallife
problems,
present computer simulations, show proofs of results… Like the content of the course, they are meant to be
open and fit individual tastes. |
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課程要求 |
Math 7509 Probability
Theory (I), or any equivalent course in
probability introducing at least the notions of random variables, expectation, conditioning,
conditional expectation, and so on, as well as the Law of Large Numbers and the Central Limit
Theorem. Martingales are introduced in Math 7509, so will be assumed to be known, but we will
give a short reminder about them.
Knowledge of measure theory is a plus, but is not necessary. |
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預期每週課後學習時數 |
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Office Hours |
另約時間 備註： Come see me anytime in my office. Email me beforehand if you want to make sure that I am available or for anything specific. |
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指定閱讀 |
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參考書目 |
None mandatory. But the course will be inspired
by Essentials of Stochastic Processes, Durrett, where additional exercises can be found. Other
good references are
● Introduction to Stochastic Processes, Lawler
● Stochastic Processes, Ross
● Probability and Random Processes, Grimmett & Stirzaker
● Markov Chains, Norris
● Probability with Martingales, Williams
● Continuous martingales and Brownian Motion, Revuz & Yor |
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評量方式
(僅供參考) |
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