ECE 604 - Stochastic Processes
Instructor
Professor
Weihua
Zhuang
Office:
EIT
4159
Phone:
extension
35354
email:wzhuang@uwaterloo.ca
Prerequisite
An introductory course in probability such as ECE 316.
Text
Sheldon M. Ross, Introduction to Probability Models, 11th edition, Academic Press, 2014.
Course Description
This course studies fundamentals in probability theory and random processes. It is strongly recommended that students in communications, networks, signal processing, control, and other related areas should take this course.
Course Outline
- Review: probability and conditional probability, random variables, probability density function, probability mass function, cumulative distribution function, mean and variance, moment generating functions.
- Convergence concepts: convergence in mean square, convergence almost everywhere, convergence in probability, convergence in distribution.
- Markov chains: Chapman-Kolmogorov equations, time reversibility, Markovian decision process.
- Poisson processes: exponential distribution, Poisson process, generalization of the Poisson process.
- Continuous-time Markov chains: birth and death process, transition probability function, time reversibility, uniformization.
- Renewal processes: limit theorems, renewal reward process, regenerative process.
- Stationary processes: Brownian motion, white noise, Gaussian process, stationary process.
Grading
Midterm Examination = 30%, Final Examination = 70%.