DEPARTMENT OF MATHEMATICS UNIVERSITY OF TEXAS AT AUSTIN
M362M: Introduction to Stochastic Processes
First-day Handout, Fall 2011
Unique course number: 55435
Class meets: TTH 8:00am-9:15am, CPE 2.210
Instructor: Mihai Sı̂rbu
Office: RLM 11.140
Office Hours: Tuesday 4:00-5:00 pm and Thursday 9:30 am-10:30 am
Phone: 512-471-5161
E-mail: [email protected]
Grader: due to limited resources, there is no grader this semester. The instructor will grade some selected problems
from the homework as described below.
Course Description: We focus on several classes of elementary stochastic processes which are often used in various
applications: random walks, branching processes and more generally discrete-time Markov chains. The goal is to provide
the student with mathematical tools and techniques necessary for understanding and successful use of stochastic models
in a variety of applications within mathematics and in science, engineering, economics, etc..
Prerequisites: Students are assumed to be familiar with the basics of probability as taught, for example, in M362
Probability, or presented in Sheldon Ross’s “First Course in Probability”; there will be little or no review. Also, a working
knowledge of multi-variable calculus and linear algebra is assumed.
Students without formal prerequisites can still enroll provided that they:
1. Come and see me in person,
2. Realize that they are responsible for all the prerequisite material, and that a portion of the first in-term exam will
cover basic probabilty theory.
Drop Dates: The last drop date for this class is the one announced on the academic calendar of the University of Texas
at Austin. See http://registrar.utexas.edu/calendars/11-12/index.html.
Textbook: Certain parts of the course follow loosely Adventures in Stochastic processes by Sidney I. Resnick (ISBN
0-8176-3591-2), but you are not required to use it as a textbook. Lecture notes will be provided by the instructor: they
are a courtesy of our colleague Gordan Žitković. If you need extra practice problems, please look at the Introduction to
Probability Models by Sheldon Ross (ISBN 978-0125980623).
Course webpage: The online course-management system Blackboard will NOT be used in this course. Instead, all the
materials will be available on http://www.math.utexas.edu/users/sirbu/M362M-Fall2011/M362M-Fall2011.html
Final Exam Date: The final exam was scheduled by the university on Saturday, December 10, 2-5 pm. Please
double check at http://registrar.utexas.edu/schedules/119/finals/
Schedule of classes and exams:
Lecture #
Date
Topic
1
Aug 25
Introduction to Probability
2
Aug 30
Introduction to Probability
3
Sep 1
Introduction to Probability
4
Sep 6
Stochastic Processes: canonical spaces
5
Sep 8
Stochastic Processes: canonical spaces
6
Sep 13
Random Walks
7
Sep 15
Simple Random Walks
8
Sep 20
Properties of Simple Random Walks
9
Sep 22
Generating Functions
10
Sep 27
Test 1
11
Sep 29
Generating Functions
12
Oct 4
More on Random Walks
13
Oct 6
More on Random Walks
14
Oct 11
Stopping Times
1
Lecture #
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Date
Oct 13
Oct 18
Oct 20
Oct 25
Oct 27
Nov 1
Nov 3
Nov 8
Nov 10
Nov 15
Nov 17
Nov 22
Nov 29
Dec 1
Topic
Branching Processes
Branching Processes
Markov Chains
Markov Chains
Markov Chains
Markov Chains
Test 2
Classification of States
Classification of States
Classification of States
Stationary Distributions
Stationary Distributions
Stationary Distributions
Test 3
Homework: A weekly (or so) homework will be assigned and its due date (typically 7 days after) will be announced
on the course web-site. Since there is no grader, a very small random subset (usually one) of the assigned problems will
be fully graded by the instructor (of course, you will not be told which ones!). No late homework will be tolerated. In
return for a strict adherence to this policy I will drop the lowest 2 homework grades. You are allowed (and encouraged) to
discuss homework problems with other students, but you have to write up the solutions yourself. Homework assignments
you turn in must be organized and stapled. The assignments must be done carefully and written legibly on standard size
paper. Box answers where possible. Staple in the top left-hand corner. Write your Name, Course Number, Assignment
Number, and Date on the first page. Put your last name on top of each page. Put solutions in order and number pages. A
portion of the hw assignment may be computer-based and you will be asked to perform simulations/computation using the
software package Mathematica. No prior experience is necessary. Familiarize yourself with the location of the computer
labs and computers with Mathematica on campus.
Exams: There will be three 75-min in-term exams (they will be administered during regular class time and the schedule
is announced in the table above), as well as a final exam (scheduled by the university during the final exam period,
please check above as well). If you miss any in-term for a documented reason (illness, approved and previously announced
religious holiday, or some other extraordinary circumstance), the in-term score will be computed as an average of the
remaining in-term exams. It is the policy of The University of Texas at Austin that the student must notify each instructor
at least fourteen days prior to the classes scheduled on dates he or she will be absent to observe a religious holiday. For
religious holidays that fall within the first two weeks of the semester, the notice should be given on the first day of the
semester. The in-terms will focus on the material covered since the last exam, while the final will be comprehensive. If
your average score on the three in-terms exceeds 90% (and you attend all three in-terms), you will be exempt from the
final exam and you will get an automatic A.
What is allowed, and what is not: You are not permitted to use the textbook, your notes or any other written material
during the in-terms or the final exam. Calculators are also generally outlawed, unless I specifically stated otherwise before
the exam. In return, I will design the exams to be hands-on without being computationally overwhelming.
Grading:
There is no curve in this class and the letter grades are assigned according to the following computation
Max Final Score
100%
Final Exam
In-terms
Homework
50%
35%
15%
Final Score
90%-100%
88%-89%
85%-87%
79%- 84%
77%-78%
74%-76%
69% - 73%
67%-68%
64%-66%
59% - 63%
55%-58%
< 55%
Letter Grade
A
AB+
B
BC+
C
CD+
D
DF
• Please do not attempt to ”bargain” for an extra 1%-2% on exams or assignments. The plus/minus grading scheme
makes sure that if you are close to an A you will not get a B but an A• If you have any complaint on grading, for either the tests or homework, you should let me know within one week
from the time the graded test/assignment was returned to you. Please do not come at the time of the final exam
complaining about Test 1: such complaints will not be admitted.
Academic (dis)Honesty: I will do everything in my power to prosecute cheaters. You are expected to have read and
understood the current issue of the General Information Catalog, published by the Registrars Office, for information about
procedures and about what constitutes scholastic dishonesty.
Also please visit http://deanofstudents.utexas.edu/sjs/acint_student.php. In a less formal, but more direct
language, if you are caught cheating, you will fail the course and be sent to the Dean of Students for further disciplinary
action - expulsion from the university is a very possible scenario.
Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. If you have a documented disability and you need special treatment as a
result of your disability, please let me know as soon as possible, but definitely within the first 3 weeks of class. For more
information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.
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