Syllabus for Math 461, Section F1 (Applied Stochastic Processes)

• Instructor: Richard Sowers
• Office: 227B Illini Hall
• Phone: (217) 333-6246
• email: r-sowers@math.uiuc.edu
• Home page:https://faculty.math.illinois.edu/~r-sowers (this syllabus can be found there)
• Office Hours: MWF 3-4 and by appointment
• Class meets: MWF 2-2:50 P.M. in 155 Altgeld Hall

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

Grades will be determined on the basis of homework questions and two exams.