Course

EE 565000

Stochastic Processes

1. Course Description

This course discusses mathematical models for physical phenomena which possess random features. Physical phenomena which occur in the study of networking, economics, finance, control, communications, signal processing, statistical physics and biological processes often present random behaviors. Stochastic processes which are useful in the modeling of these random phenomena will be discussed, including point processes, Markov processes, martingales and Brownian motion. This course requires knowledge on calculus and elementary probability theory.

2. Text Book

S. M. Ross, Stochastic Processes, 2nd edn. John Wiley & Sons, Inc., 1996.

3. Reference

I.		Probability Theory
I.1		S. Ross, A First Course in Probability, 8th edn. Prentice Hall, 2010.
		(a very good first course on this subject)
I..2		K.-L. Chung, A Course in Probability Theory, 2nd edn.
		New York: Academic Press, 1974. (highly recommended)
I..3		A. N. Shiryayev, Probability. New York: Springer-Verlag, 1984. (chapters 1-4)
I..4		C.-C. Lu, Lecturenotes on Stochastic Processes. Department of Electrical
		Engineering, National Tsing Hua University, 2009. (chapter 1)

II.		Stochastic Processes
II.1		E. Cinlar, Introduction to Stochastic Processes. Englewood Cliffs, NJ: Prentice-Hall Inc., 1975.
II.2		E. Wong and B. Hajek, Stochastic Processes in Engineering Systems. New York: Springer-Verlag, 1985.
II.3		J. Lamperti, Stochastic Processes. New York: Springer-Verlag,1977.
II.4		A. N. Shiryayev, Probability. New York: Springer-Verlag, 1984. (chapters 5-8)

4. Teaching Method

This is an English–teaching course. After a review on essentials of probability theory in the first chapter of the textbook by Ross, we will cover Poisson process and renewal theory (Chapters 2 and 3 of Ross) before the first midterm in early November. Then we will continue to cover discrete-time Markov chains and continuous-time Markov chain (Chapters 4 and 5 of Ross) before the second midterm in mid December. Finally we will study martingale theory with applications to random walks, Brownian motion and Markov processes before the final exam in mid January. Homeworks will be assigned weekly, graded and can be retrieved from my web site. And homework solutions will be distributed in the classroom.

5. Schedule

1.		A review of probability theory (3 weeks)
2.		The Poisson process (2 weeks)
3.		Renewal theory (2 weeks)
4.		Discrete-time Markov chains (3 weeks)
5.		Continuous-time Markov chains (2 weeks)
6.		Martingales (2 weeks)
7.		Random walks (1 week)
8.		Brownian motion and Markov processes (1.5 weeks)

6. Exercise and Homework

#	Homework Assignment	Upload date
1.	HW01	2012/10/01
2.	HW02	2012/10/01
3.	HW03	2012/10/08
4.	HW04	2012/10/20
5.	HW05	2012/10/20

7. Quiz (Problems and Solutions)

#	Problems and Solutions	Upload date
1.

8. Teaching Assistants

	E-mail	TA Time	Office	Phone
陳文燿	wychen@abel.ee.nthu.edu.tw		EECS608	34032
葉力嘉	lcyeh@abel.ee.nthu.edu.tw		EECS608	34032