**Class time and place:**11:00-12:20 MW, 1015 ECEB**Instructor:**Prof. Olgica Milenkovic 311 CSL, milenkov at illinois dot edu

Office Hours: Mondays 1:30-3:00 in 311 CSL**Teaching Assistant:**Xiaobin Gao, xgao16 at illinois dot edu

Office hours: Tuesdays 4-6 pm in 368 CSL except for February 7, March 7, and April 11, when the office hours will be held in 154 CSL

- There will be an in-class quiz on Monday, February 6th. The quiz will cover material from ECE 313 (or an equivalent course) and Chapter I of the text.

- There will be a recitation on Monday, January 30th, at 6:30pm, Room 2017 ECEB.

- There will be a recitation section on Monday, February 13th, at 6:30pm, Room 2017 ECEB. The recitation will cover examples from Chapter 2.

- There will be a new grading policy for the homework, starting with hw2: The TA will randomly select half of the problems for grading and your score will be solely based on your solutions for the selected problems. Please make sure to attempt to solve every problem!
- There will be a review section for Exam 1 on Monday, March 6th, at 6:30pm, Room 2017 ECEB.
- There will be a
**review section for Exam 2**on Monday, April 17th, 8:30-9:30pm, Room 3017 ECEB.

- The problems (on textbook) that have been/will be covered during the recitations: 1.13, 1.22, 1.31, 1.33, 2.2(a), 2.4(a)(b), 2.8, 2.9, 2.31, 3.19, 3.31, 4.9, 4.15, 4.17

- Exam 1 will be held on March 7th, ECEB 2017, 7-10pm. PLEASE HOLD THE DATE. You will be allowed one sheet of notes (8.5''x11'', both sides) for the exam. Otherwise the exam is closed book.
- Exam 2 will be held on April 19th, 7-9pm,
**ECEB****3017**. You will be allowed two sheets of notes (8.5''x11'', both sides) for the exam. Otherwise the exam is closed book. - The Final Exam will be held on May 11, 2017, from 8am until 11am. The classroom will be announced in March. You will be allowed three sheets of notes (8.5''x11'', both sides). Otherwise the exam is closed book.

- Lectures - Ch1-Ch2
- Lectures Ch2
- HW 1
- Quiz
- Solutions for the Quiz
- HW 2
- Terry Tao's blog on the LLN
- HW 3
- Lectures - Ch3 (without Kalman filtering)
- Lectures - Kalman filtering and Chapter 4
- Midterm 1
- HW 4
- HW 5
- Lectures - Markov Processes
- Lecture - The EM algorithm
- HW 6

- Exam 1 Spring 06 and its solution
- Exam 1 Fall 05 and its solution
- Exam 1 Fall 09 and its solution
- Exam 2 Fall 09 and its solution
- Exam 2 Spring 04 and its solution
- Exam 2 Spring 07 and its solution
- Final Fall 09 and its solution
- Final Spring 04 and its solution
- Final Spring 03 and its solution

**Syllabus:**This is a graduate-level course on random (stochastic) processes, which builds on a first-level (undergraduate) course on probability theory, such as ECE 313. It covers the basic concepts of random processes at a fairly rigorous level, and also discusses applications to communications, signal processing, control systems engineering, and computer science. 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.Topics to be covered include:

- Probability Review;
- Convergence of a Sequence of Random Variables;
- Minimum Mean Squared Error Estimation;
- Jointly Gaussian random variables and vectors;
- Random Walks and Brownian Motion;
- Discrete-Time Markov Chains;
- Continuous-Time Markov Chains and Poisson Processes;
- Stationarity, WSS and Ergodicity;
- Martingales and the Azuma-Hoeffding Inequality;
- Random Processes Through Linear Systems;
- Kalman and Wiener Filtering;
- Other topics as time permits.

**Required Text:**B. Hajek, Random Processes for Engineers, Cambridge 2015. A soft copy of the book can be downloaded here. Preprints are also available through the ECE Store. I will also make frequent use of other texts, for example The Theory of Probability, by Santosh S. Venkatesh. See the Grainger Library reserves below.**References in Grainger Library:**

Papoulis, A.; Probability, Random Variables, and Stochastic Processes

Wong, Eugene; Introduction to Random Processes

Wong, E./Hajek, B.; Stochastic Processes in Engineering Systems

Stark, H./Woods, J.; Probability, Random Processes, and Estimation Theory

Feller, W.M.; An Introduction to Probability Theory and its Applications

Rudin, Walter; Principles of Mathematical Analysis

Grimmett, G. R./Stirzaker, David R.; Probability and Random Processes

Gallager; Discrete Stochastic Processes Santos Venkatesh, The Theory of Probability**Exams, homework, grading, etc.:**- There will be approximately 7 Homework assignments. Collaboration on the homework is permitted, however each student must write and submit independent solutions. Homework is due within the first 5 minutes of the class period on the due date. No late homework will be accepted (unless an extension is granted in advance by the instructor).

- There will be two mid-term exams and one final. The dates will be announced shortly.

- You may bring one sheet of notes to the first hour exam, two to the second hour exam, and three to the final exam. You may use both sides of the sheets, the sheets are to be standard US (letter paper) or European (A4) size with font size 10 or larger printing (or similar handwriting size). The examinations are closed book otherwise. Calculators, laptop computers, tables of integrals, etc. are not permitted.

- Your course grade will be determined by your performance in the H, M1, M2 and F, according to the formula:

Score = .2H + max{.15M1 + .15M2 + .5F, .25M1 + .15M2 + .4F, .15M1 + .25M2 + .4F},

where H, M1, M2 and F are normalized to 100.