Term
and
Year
of
Offering:
Fall
2013
Course
Number
and
Title:
ECE
604
Stochastic
Processes
Lecture
Times,
Building
and
Room
Number:
Mondays,
2:30pm-5:20pm,
EIT
3151
Instructor's
Name:
Ravi
Mazumdar
Office
Location
and
phone:
EIT
4011,
(519)888-4567
x37444
Office
Hours:
When
not
busy
in
my
office
or
by
appointment
(please
send
me
an
e-mail
to
set
up
an
appointment).
Email
Contact:
mazum@ece.uwaterloo.ca
Class
website:
https://ece.uwaterloo.ca/~mazum/ECE604/
Pre-requisite:
ECE316
or
an
undergrad
probability
course
Aims: Stochastic processes is a core course for graduate studies in electrical engineering and a must for those who wish to specialize in communications, controls, signal processing, and networking. The subject matter is also very useful and really quite interesting.
The principal aim of this course is to introduce the students to a rigorous and fairly comprehensive view of probability, random variables and random signals (or stochastic processes). The first part of the course will begin with a comprehensive view of probability and random variables. The notions of conditional probabilities and expectations will be studied. Once the basics have been seen we will then study important results needed in the study of random phenomena as they present themselves in the modeling of signals and noise namely the notions of independence, normality etc. Based on these we will then study key results such as the Central Limit Theorem, Laws of Large Numbers and converegence concepts. The latter third of the course will be devoted to the study of important signal models especially the so-called theory of wide sense stationary processes. The course will conclude with an introduction to Markov chains.
The overall aim is to provide the student with a good understanding of the underlying structure associated with stochastic processes and gain the necessary background to have a solid foundation to work in applications involving stochastic phenomena.
Course Outline
- Review of Probability: Distributions, Expectations, Conditioning, Bayes' Theorem, Independence, Random Variables, Bounds: Markov, Chebychev, Chernov. Borel-Cantelli Lemmas.
- Gaussian Random Variables, Conditioning, Conditional Expectation
- Stochastic Processes : Classification: Gaussian, Poisson, Markov, Stationarity- Weak and strong laws. CLT, Convergence, Ergodic Theorems.
- Wide sense stationary processes- L2- Theory of Stochastic Processes: Bochner’s Theorem, Spectral Theory, Shannon sampling, Karhunen-Loeve Expansions. AR and MA Approximations. Wold decomposition and prediction of 2nd. order stationary processes.
- Independent increment processes: Wiener process, Poisson Processes. Gauss-Markov processes.
- Introduction to Markov chains: Classification, invariant distributions, ergodicity.
- Introduction to martingales- the discrete-time case. Martingale convergence theorem. Doob's optional sampling. Wald's lemma. (If time permits)
Text and References
There is no text for this course. Typed class notes are available on the website. The following references are useful to expand on the notes:
References:
There
are
a
number
of
books
that
cover
the
material
but
with
variable
treatment
of
the
topics.
S.
M.
Ross:
Introduction
to
Probability
Models,
4th
Edition,
Academic
Press,
1989
(good
for
refreshing
probability
but
lacks
wide
sense
theory)
G.
Grimmett
and
D.
R.
Stirzaker:
Probability
and
random
Processes,
3rd.
Edition,
Cambridge
University
Press,
2002.
(excellent
book
but
a
bit
advanced
and
not
enough
on
wide-sense
theory)
Course Evaluation
Weekly
problem
sets
will
be
posted
on
the
website.
The
onus
is
on
you
all
to
attempt
them.
Solutions
will
be
posted
after
2
weeks.
There
will
be
a
midterm
examination
and
a
final
exam.
The
dates
will
be
announced
later.
Marks
distribution:
Midterm=
45%,
Final
Exam
=
55%
Auditors will be required to take the midterm exam and achieve a pass mark.
Additional remarks
- All exams will be closed book. You will be allowed to bring in one page of summary.
- If you miss the midterm exam no make-up exam will be given. If you have a valid reason then your final marks will be based on your performance in the rest of the course.
- Students are advised to be regular and attempt the problem sets.
- Dishonesty will be dealt with harshly according to the rules of the university.