Math 2940: Applied Stochastic Methods Spring 2013
Instructor: David
Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
MWF 9:009:50pm, Thackeray 525
Office
Hours: MW 1:303:00pm, Thackeray 511,
or by appointment.
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math2940.html
Course Description
In this
course we will discuss the fundamental theory and applications of stochastic
processes. The topics will include continuous/discrete state and
continuous/discrete time Markov chains, with specializations for birth and
death processes, and basic stochastic differential equations. We will use both
analytical and computational tools. Most of the applications will be in
biology, chemistry or physics.
Prerequisites
Advanced
calculus (Math 1530, or equivalent) including Riemann and Lebesgue
integral, Linear algebra (Math 1180, 1185 or equivalent) including eigenvalue
and eigenvector analysis.
Textbook
Linda J.S.
Allen: An Introduction to Stochastic Processes with Applications to Biology,
Second Edition, CRC Press, 2011. ISBN:9781439818824
Additional Suggested Reading
E. Parzen, Stochastic
Processes, SIAM 1999.
C. W.
Gardiner, Handbook of Stochastic Methods,
Springer 2004.
N.G. van Kampen, Stochastic
Processes in Physics and Chemistry, Elsevier, 1992.
E. Nummelin, General
Irreducible Markov Chains and Nonnegative Operators, Cambridge University
Press, 1984.
S.P. Meyn & R.L. Tweedie, Markov Chains and Stochastic Stability,
Springer, London, 1993.
Grading
Scheme
Homework
Assignments: 30%
Midterm
Exam: 30%
Final
Exam: 40%
Disability Resource Services
If
you have a disability for which you are or may be requesting an accommodation,
you are encouraged to contact both your instructor and Disability Resources and
Services, 140 William Pitt Union, 4126487890 or 4123837355 (TTY) as early
as possible in the term. DRS will verify your disability and determine
reasonable accommodations for this course.
Academic Integrity
Cheating/plagiarism will not be tolerated. Students
suspected of violating the University of Pittsburgh Policy on Academic Integrity
will incur a minimum sanction of a zero score for the quiz, exam or paper in
question. Additional sanctions may be imposed, depending on the severity of the
infraction. On homework, you may work
with other students or use library resources, but each student must write up
his or her solutions independently. Copying solutions from other students will
be considered cheating, and handled accordingly.
Syllabus
Week 
Reading 
Topics 
Homework 
Notes 
Jan
7 – Jan 11 
1.11.6 
Review
of Probability Theory, distributions, generating functions, Central limit
theorem, stochastic processes 


Jan
14 – Jan 18 
2.12.5 
Discretetime
Markov chains, first passage time 


Jan
21 
NO
CLASSES 


Jan
23 – Jan 25 
2.62.10 
Stationary
probability distribution, MC simulation, random walk in 2D and 3D 


Jan
28 – Feb 1 
3.13.8 
Restricted
random walk, selfavoiding walk, absorbing boundary, reflecting boundary 

Feb
4 – Feb 8 
Convergence
rate, Random walks on groups, card shuffling 

Feb
11 – Feb 15 
Metropolis
algorithm, 

Feb
18 – 22 
5.15.6 
Continuous
time MarkovChains, Poisson process 


Feb
25 – Mar 1 
5.75.11 
Kolmogorov
differential equation, Generating
function technique Midterm Exam 


Mar
4 – Mar 8 
6.16.11 
Birth
and death processes, First passage time 


Mar
11 – Mar 15 
SPRING
BREAK 


Mar
18 – Mar 22 
7.17.8 
Applications
of continuoustime Markov chains Gillespie
algorithm 


Mar
25 – Mar 29 
8.18.5 
Diffusion
processes, boundary conditions, eigenfunction
method 


Apr
1 – Apr 5 
8.68.10 
Wiener
process, Ito integral, Stochastic differential equations 


Apr
8 – Apr 12 
9.19.5 
Numerical
methods, Applications of SDEs 


Apr
15 – Apr 19 
9.69.9 
Applications
of SDEs, Review 




