EE 640 Stochastic Systems

Spring 2013


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Visit course website at

and the course site in Blackboard.


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Instructor: Dr. Sen-ching Cheung (cheung at



Room 217 Marksbury (859-218-0299)

By appointment or try your luck

FPAT 469

TTh 9-11am

Teaching Assistant: Wanxin Xu (wxbit0930 at



FPAT 669

M and F 11a – 12p


Class Schedule


Lecture:           TTh      11:00am-12:15pm (FPAT 265)

Final:               4/30     10:30am-12:30pm (FPAT 265)          


Course Description

(From University Bulletin) Random variables, stochastic processes, stationary processes, correlation and power spectrum, mean-square estimation, filter design, decision theory, Markov processes, Simulation


(From Instructor) This is a graduate-level course on random (stochastic) processes, which builds on a first-level (undergraduate) course on probability theory, such as MA 320. It covers the basic concepts of random processes at a theoretically rigorous manner, and also discusses applications to communications, signal processing and control systems engineering. To follow the course, in addition to basic notions of probability theory, students are expected to have some familiarity with the basic notions of sets, sequences, convergence, linear algebra, linear systems, and Fourier transforms.


Tentative Syllabus


Week 1

Mathematical preliminaries (ch. 1)

Week 2

Review of probability theory (ch. 1)

Week 3

Convergence of random variables (ch. 2)

Week 4

Limit theorems and Large Deviation (ch. 2)

Week 5

Joint Gaussian Distribution and Orthogonal Principle (ch. 3)

Week 6

Kalman Filtering (ch. 3)

Week 7

Review and Exam 1

Week 8

Random Process I (ch. 4)

Week 9

Random Process II (ch. 4)

Week 10

Differentiation and Integration of Random Processes (ch. 7)

Week 11

Karhunen-Loeve Decomposition (ch. 7)

Week 12

Stochastic Linear System (ch. 8.1-8.3)

Week 13

Optimal Wiener Filtering (ch. 9)

Week 14

Discrete Markov Chain (ch. 6)

Week 15

Review & Final Exam

Expected outcomes of student learning

  1. To be comfortable in probability spaces, random variables and commonly used distributions.
  2. To have a solid understanding of different types of convergence of random variable sequence.
  3. To use multivariate random variables and calculate minimum mean square error estimation including discrete-time Kalman Filter.
  4. To have a broad understanding of different types and properties of random processes
  5. To model and manipulate discrete-state stochastic systems with Markov chains
  6. To have a solid understanding of basic calculus of continuous random processes
  7. To model and manipulate continuous-time stochastic linear system including Wiener Filter


Your grade will be based on:


Weekly Homework




Comprehensive Final



  1. Homework

-          Homework will be assigned weekly through the Blackboard site.

-          While you can discuss with others, you must do your own work.

-          Late homework will not be accepted without prior notice.

  1. Midterms and Final

-          All exams will be closed book.

-          Two double-sided chat sheets are allowed for midterm, four sheets for final.

-          Make-up test will only be given upon permission from the instructor prior to the test.

  1. Grade Assignment

-          The letter grade assignment is based on the following scale:

From 90 to 100 pts => A, from 75 to 89 pts. => B, from 60 to 74 pts => C, from 0 to 59 pts. => E.   

4.       Academic honesty

-          I have a zero-tolerance policy for all forms of plagiarism and cheating, from copying a homework answer from your friend to cheating in the exams. Not only you will lose all the points for that assignment, the incident will also be reported to the Department.



B. Hajek. 2011. An Exploration of Random Processes. Free online at

References (All are available on reserve in engineering library and those underlined are highly recommended):

1.      R. D. Yates and D. J. Goodman. 2005. Probability and Stochastic Processes (2nd Edition). Wiley.

This book provides a less rigorous and comprehensive treatment than Hajek but has extensive and concrete examples. It is highly recommended as background reading material, especially for those who are less fluent mathematically.

2.      A. Papoulis and S. U. Pillai. 2002. Probability, Random Variables and Stochastic Processes (4th Edition). McGraw Hill.

This book is a classical text book for graduate-level stochastic systems. It is an excellent reference for this class.

3.      J. S. Rosenthal. 2006. A First Look at Rigorous Probability Theory (2nd Edition). World Scientific.

This short book provides a measure-theoretical treatment of probability theory and random processes that goes slightly beyond the scope of this class. It is highly readable and is recommended for further studies.

4.      K. S. Shanmugan and A. M. Breipohl. 1988. Random Signals: Detection, Estimation and Data Analysis. John Wiley & Sons.

This book is the text used in past semesters.


1.       MA 320 or proficiency in basic discrete probability

-          I definitely recommend the following review by Randall Berry:

2.       EE 421 or good knowledge about signals and system

-          You might want to glance through my old class notes at

3.       MA 471G (desirable but not necessary)

-          Page 1-60 of the following online book provides a nice foundation of  elementary mathematical analysis for this class:

-          At the very least, you should be comfortable with Appendix A of the reference 4 above. A hard copy of appendix A will be provided to you during the first day of lecture.

4.       Matlab

Sen-ching Samson Cheung

Last modified: 1/8/2013 11:06:25