Fall 2013 Course Syllabus: MATH 691.101
Course Title:
Stochastic Processes
Textbook:
An Introduction to Stochastic Modeling, by Mark A.
Pinsky and Samuel Karlin; Publisher: Academic Press, 4th
edition; ISBN: 978-0-12-381416-6.
Reference Books:
Prerequisites:
Chiang, C.L. (1980). An Introduction to Stochastic Processes and
Their Applications, Krieger, NY
Longini, I.M. and Hudgens, M.G. (2012). Lecture Notes on
Stochastic Processes in Biostatistics: Applications to Infectious
Diseases (On the web). Lecture Notes
Guttorp, P. (1995). Stochastic Modeling in Scientific Applications,
Chapman & Hall
Math 662 or equivalent with Departmental appoval
Course Description: Renewal theory, renewal reward processes and applications.
Homogeneous, non-homogeneous, and
compound Poisson processes with illustrative applications. Introduction to Markov
chains in discrete and continuous time with
selected applications.
Course Outline:
Date Lecture
Topic
Discrete
Time
Markov
Chains
Week
1
Definitions, Transition probability matrices, Introductory
1
examples
First step analysis, some special Markov chains (The
two-state Markov chain, one dimensional
random walk, Markov chains defined by independent
random variables)
Discrete Time Markov Chains (continued)
Success runs, functionals of random walks and
success runs
Week
2
2
Week
3
3
Discrete Time Markov Chains (continued)
Branching processes, long run behavior, limiting
distribution, examples
Week
4
4
Discrete Time Markov Chains (continued)
The classification of states (recurrent and transient), the
basic limit theorem
Assignment
Homework 1
Homework 2
5
Poisson Processes
Week
6
6
Definitions, nonhomogeneous processes, Cox
processes, the law of rare events
Midterm Exam 1(Wednesday, 10/09/13)
Poisson Processes (continued)
Distributions associated with the Poisson process
Week
7
7
Poisson Processes (continued)
The uniform distribution and the Poisson process,
compound and Marked Poisson processes
Week
8
8
Continuous Time Markov Chains
Pure birth processes, pure death processes, birth and
death processes
Week
9
9
Midterm Exam 2(Wednesday, 10/30/13)
Continuous Time Markov Chains (continued)
Differential equations of birth and death processes
Week
10
10
Continuous Time Markov Chains (continued)
The limiting behavior of birth and death processes.
Birth and death processes with absorbing states
Week
11
11
Week
12
12
Week
13
13
Week
14
14
Renewal Phenomena
Definition of a renewal process and related concepts,
examples. The Poisson process viewed as a renewal
process
Renewal Phenomena (continued)
The elementary renewal theorem, the renewal theorem
for continuous lifetimes. Asymptotic distributions, age
and excess life
Renewal Phenomena (continued)
Delayed renewal processes, stationary renewal
processes, cumulative and related
processes, the discrete renewal theorem
Review for final exam
Week
5
Week
15
FINAL EXAM:
Wednesday ~ December 18, 2013
IMPORTANT DATES
FIRST DAY OF SEMESTER
LAST DAY TO WITHDRAW
LAST DAY OF CLASSES
FINAL EXAM PERIOD
September 3, 2013
November 4, 2013
December 11, 2013
December 13 – 19, 2013
Homework 3
Homework 4
Homework 5
Homework 6
Grading Policy
Assignment Weighting
Homework
30 %
Midterm Exam 1
20 %
Midterm Exam 2
20 %
Final Exam
30 %
Instructor:
Contact Information:
Office Hours:
Tentative Grading Scale
A
90 -- 100
B+
84 -- 89
B
78 -- 83
C+
72 -- 77
C
60-- 71
F
0 -- 59
Prof. Seonja Kim
211F Cullimore Hall
973-596-5374
sjkim@njit.edu
Monday 12:30 – 2 pm
Thursday 6 – 7:30 pm
Plus by appointment
Or follow the link
http://math.njit.edu/students/officehours.php
NOTE : This syllabus is subject to (reasonable) changes at the discretion of the
instructor and with advance notice to you.
Important Departmental and University Policies
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Academic Integrity Code
http://www.njit.edu/academics/pdf/academic-integrity-code.pdf
Prerequisites Requirements are Enforced
Attendance is Required in Lower-Division Courses
Exam Policies (No Make Up Exams and More)
Cell Phone and Pager Use Prohibited in Class
Complete DMS Course Policies
(math.njit.edu/students/undergraduate/policies_math)