ECE1500F - Stochastic Processes, Fall 2009

Description: An introduction to stochastic processes and probabilistic modeling with emphasis on communication system applications.

Prerequisites: Introductory probability and linear systems, or consent of instructor.

Textbooks: A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, Fourth Edition, McGraw-Hill, ISBN  0-07-366011-6 (Required); A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Third Edition, Addison Wesley, ISBN-10: 0131471228, ISBN-13: 978-0131471221 (Recommended).

Course Website:
Public access: http://www.comm.utoronto.ca/~liang/courses/ECE1500FA09/
Login required: ECE1500 course website on Blackboard through the UofT Portal

Instructor: Ben Liang
Office: Bahen Centre Room 4122 (through doors 4113 or 4145)
Contact: http://www.comm.utoronto.ca/~liang

TA: Hossein Seyedmehdi, BA4000, hossein@comm.utor...

Lectures:
Tuesdays 4 - 6 pm, BA1210
Thursdays 2 - 3 pm, BA1240

Office Hours:  
Thursdays 3 - 4 pm, BA4122

Grading Policy: There will be bi-weekly homework assignments, one midterm exam, and one final exam.  The weights for different grading components:
Homework 10%
Midterm Exam 40%
Final Exam 50%

The homework assignments can be found here.  Homework will be graded solely on the basis of effort, not correctness. Solution to the homework problems will be available on the Blackboard course website when they are due, usually two weeks after they are assigned.

Topical Outline: (A weekly updated lecture schedule can be found here.)

• Probability Theory Overview - axioms of probability, repeated trials, conditional probability, random variables, characteristic functions (2 weeks)
• Sequence of Random Variables - joint statistics, conditional statistics, stochastic convergence, law of large numbers, central limit theorem (1 week)
• Stochastic Processes - definitions and interpretations, classical examples, statistics, stationarity, ergodicity, system with stochastic inputs, power spectrum, Fourier series and Karhunen-Loève expansion (3.5 weeks)
• Mean Square Estimation - orthogonality principle, linear mean square estimation, geometric interpretation, Wiener filtering (1 week)
• Discrete-Time Markov Chain - classification, Chapman-Kolmogorov equations, stationary distribution, limiting distribution, absorption probabilities, mean absorption time, branching (2 weeks)
• Continuous-Time Markov Chain - sojourn time, transition rates, birth-death processes, Markovian queues, time reversibility (1.5 weeks)