Type of Credit: Partially Required
Credit(s)
Number of Students
To introduce fundamental concepts of Probability theory including Strong law of large numbers, Central limit theorem, Martingale theory and Infinitely divisible laws.
Students will be able to manipulate basic tools like independence, convergence and asymptotic analysis after the course.
The class will meet three hours in the class room per week. There will be exercises every week and a final exam.(50% each).
Office hours is from 12:00 to 3:00pm every Friday.
Reference books: ( Ref 1)Probability with Martingales, D. Williams Statistical Laboratory, DPMMS, Cambridge University, 1991.
(Ref 2)Probability Essentials by J.Jacod and P.Protter.Springer, 2000, 2nd edition.
(Ref 3) Probability: Theory and Examples by R. Durrett, Duxbury Press, 1995.
能力項目說明
Fundamental concepts and basic knowledge in analysis and Probability theory will be introduced. Student should be able to handle and formulate mathematical problems independently. They will have enough background for more advanced or applied courses in statistics and probability theory.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
week 1. Rerview of measure theory and Monotone class theorem. 3hrs.
week 2,3, Review of conditional expectation and independent random random variables. 5hrs.
week 4,5. weak and strong law of large numbers. 6hrs.
week 6, Characteristic functions and weak convergence. 6hrs.
week 7,8, Gaussian distribution and Cenral limit theorem 6hrs.
week 9 ,Stable distributions (I) 15hrs. Ref 3. 149-160.
week 11,12, Stable distributions (II)
week 13, Hilbert spaces. 5hrs. Ref.1, P185-191.
week 14 -16, Martingale theory. 15hrs. Ref 2, P193-237
week 17, Radon-Nykodym theorem. 5hrs. Ref.1, P239-247.
week 18, Final exam.
本課程無涉及 AI 使用。
Home work 60%
Final exam 40%
Reference books:
Probability with Martingales, D. Williams Statistical Laboratory, DPMMS, Cambridge University, 1991
Probability Essentials , J. Jacod and P. Protter.Springer, 2000, 2nd edition.
Probability: Theory and Examples by R. Durrett, Duxbury Press, 1995.