STAT 580: Stochastic Processes
- Ivan Mizera
Office hours: Tuesday and Thursday 12:30 - 13:30, and also after
15:20, if there is interest; otherwise by appointment
- TIME AND VENUE
- TR 14:00-15:20
CAB 457 (Sec A1)
- CALENDAR DESCRIPTION AND PREREQUISITES
Elements of stochastic processes. Discrete and continuous time Markov
Chains; Birth and Death processes. Branching processes. Brownian
Motion. General Stationary and Markov processes. Examples.
Prerequisite: STAT 471 or consent of Instructor.
- COURSE OBJECTIVES
Teach working knowledge of several types of stochastic processes: in
particular, discrete and continuous Markov chains; certain point
processes; and finally Gaussian processes with special emphasis on the
Wiener process (Brownian motion) and stochastic integration.
There is no single followed or required text. Useful sources for the
technical details like statements and proofs of theorems, and also for
additional exercises, are:
The summaries of the results appearing in the lectures will be
provided online; these documents sometimes serve as lecture notes, but
more often constitute rather a handy study review.
Probability and Random Processes (Third Edition), by Geoffrey R. Grimmett
and David R. Stirzaker, Oxford University Press, 2001.
Introduction to Stochastic Processes (Second Edition), by Gregory F.
Lawler, Chapman & Hall/CRC, 2006.
A First Course in Stochastic Processes (Second Edition), by Samuel
Karlin and Howard M. Taylor, Academic Press, 1975.
A Second Course in Stochastic Processes, by Samuel
Karlin and Howard M. Taylor, Academic Press, 1981.
Stochastic Processes, by Joe L. Doob, Wiley, 1953.
- General aspects of stochastic processes: finite-dimensional
distributions, sample paths
- Discrete Markov chains: classification of states, large-time behavior
- Conditional expectations and martingales
- Continuous Markov chains: Poisson process, birth-and-death processes
- Renewal processes, elementary queueing
- Gaussian processes: theory, examples
- Brownian motion and elements of stochastic calculus
- GRADING POLICY
The cumulative score will be computed from the performance
in assignments (40%) (7-9 almost weekly assignments) midterm exam
(20%) and the final exam (40%). This score will determine
the final grade in the following manner: those who achieve 90% or
more will get A; 76% or more qualifies
for B; 60% or more guarantees C. Fine
distinctions (+ and -) will be determined from the relative position
of the student's score in class; also, one or several of the above
cutpoints may be lowered if class circumstances render it necessary.
Grades are unofficial until approved by the Department and/or Faculty
offering the course. Samples of past or representative evaluative
course material will be made available through the course web page.
- CLASS PARTICIPATION
Students are supposed to attend all classes and actively participate
in discussions and other class activities.
Students may use any notes written by their own hand; no other paper
materials are allowed, especially no printed ones (books, photocopies,
computer printouts). No access to the internet is allowed either; to
prevent misunderstandings, cellphones, laptops and similar electronic
devices are not to be brought to the exams. The exams will concentrate
on the correct understanding of the material, testing it on suitable
problems; therefore it is highly recommended that students work
independently on the homework assignments and complement those by
other exercises if necessary (starting from working out easy details
in the lectures and summaries of results). The examinations will not
involve any computational problems; however, computational assignments
are deemed to be very helpful for gaining the proper understanding of
the course material, and therefore are highly recommended.
Some part of the homework will involve exercises in computer
generation of various stochastic processes, in a hope to bring deeper
understanding of their underlying mechanism in this way. Students will
thus have to do some, albeit simple, nevertheless programming, and
possibly graphing of the result, in a computer language that
facilitates such tasks, and the generation of (pseudo-)random numbers.
The choice of software is not prescribed: R, Matlab, in past
Mathematica and Maple, and recently also Python were successfully used
by students in this course. The instructor is capable of providing the
support in R and Matlab; the examples in the lectures will be mostly
- IMPORTANT DATES
Midterm exam: Tuesday, Oct 24, 2016, class time (2:00-3:20) and venue
FOR THE INFORMATION ABOUT THE FINAL EXAM: FOLLOW BEAR TRACKS.
- FINE PRINT (OBLIGATORY ANNOUNCEMENTS)
There are no deferred term exams. A student who cannot write a term
examination or complete a term assignment because of an incapacitating
illness, severe domestic affliction or other compelling reasons can
apply for a deferral of the weight of the missed work to the final
exam. To apply for an excused absence, a student must inform the
instructor within two working days following the scheduled date of the
term work or term exam missed, or as soon as the student is able,
having regard to the circumstances underlying the absence. In all
cases, instructors may request adequate documentation to substantiate
the reason for the absence at their discretion. An excused absence is
a privilege and not a right; there is no guarantee that an absence
will be granted. Misrepresentation of Facts to gain a deferral is a
serious breach of the Code of Student Behaviour.
A student who
cannot write the final examination due to incapacitating illness,
severe domestic affliction or other compelling reasons can apply for a
deferred final examination. Students who failed at the start of term
to request exam accommodations for religious beliefs are expected to
follow the normal deferred final examination process. Such an
application must be made to the student's Faculty office within two
working days of the missed examination and must be supported by a
Statutory Declaration (in lieu of a medical statement form) or other
appropriate documentation (Calendar section 23.5.6). Deferred
examinations are a privilege and not a right; there is no guarantee
that a deferred examination will be granted. Misrepresentation of
Facts to gain a deferred examination is a serious breach of the Code
of Student Behaviour. If granted, the deferred final exam will be held
9:00 to 12:00 (registration 8:30) on Saturday, January 13,
2018, CAB 357.
A student who writes the final examination and fails the course may
apply for a re-examination. Re-examinations are rarely granted in the
Faculty of Science. These exams are governed by University (Calendar
section 23.5.5) and Faculty of Science Regulations (Calendar section
192.5.3). Misrepresentation of Facts to gain a re-examination is a
serious breach of the Code of Student Behaviour.
The University of Alberta is committed to the highest standards of
academic integrity and honesty. Students are expected to be familiar
with these standards regarding academic honesty and to uphold the
policies of the University in this respect. Students are particularly
urged to familiarize themselves with the provisions of
of Student Behaviour and avoid any behaviour which could
potentially result in suspicions of cheating, plagiarism,
misrepresentation of facts and/or participation in an offence.
Academic dishonesty is a serious offence and can result in suspension
or expulsion from the University. All forms of dishonesty are
unacceptable at the University. All forms of dishonesty are
unacceptable at the University. Any offense will be reported to the
Senior Associate Dean of Science who will determine the disciplinary
action to be taken. Cheating, plagiarism and misrepresentation of
facts are serious offenses. Anyone who engages in these practices will
receive at minimum a grade of zero for the exam or paper in question
and no opportunity will be given to replace the grade or redistribute
the weights. As well, in the Faculty of Science the sanction for
cheating on any examination will include a disciplinary failing grade
(NO EXCEPTIONS) and senior students should expect a period of
suspension or expulsion from the University of Alberta.
Electronic equipment cannot be brought to the examination rooms. Cell
phones are to be turned off during lectures, labs and seminars. Cell
phones are not to be brought to exams. Audio or video recording,
digital or otherwise, of lectures, labs, seminars or any other
teaching environment by students is allowed only with the prior
written consent of the instructor or as a part of an approved
accommodation plan. Student or instructor content, digital or
otherwise, created and/or used within the context of the course is to
be used solely for personal study, and is not to be used or
distributed for any other purpose without prior written consent from
the content author(s).