Syllabus for Math 461, Section F1 (Applied Stochastic Processes)
Course
topic: Applied Stochastic Processes
Text: Norris, Markov Chains, 1997, Cambridge University
Press.
Outline: This is a graduate course on Markov chains and Markov
processes.
The goal of this course is fairly rigorous understanding of Markov chains
and Markov processes. We will go through Norris' book fairly linearly,
and will especially focus on functional-analytic concepts relating to Markov
chains, augmenting the text when necessary. Below is a rough and
unordered list of some of the topics we will cover.
-
Strong Markov properties
-
Recurrence and transience
-
Invariant distributions
-
Convergence and ergodicity
-
Time reversal
-
Q-matrices
-
Holding times
-
Poisson Processes
-
Forward and Backward Equations
-
Martingale problems
-
Queuing networks
-
Markov decision processes
-
Markov Chain and Monte Carlo techniques
The goal of this course is fairly rigorous understanding of Markov chains
and Markov processes. We will go through Norris' book fairly linearly,
and will especially focus on functional-analytic concepts relating to
Markov chains, augmenting the text when necessary.
Grades will be determined on the basis of homework questions and two
exams.
Richard Sowers
(Home Page)
Department of
Mathematics
University of Illinois
at Urbana-Champaign
1409 W Green St.
Urbana, IL 61801
r-sowers@math.uiuc.edu
(217) 333-6246