Math 5050: Stochastic Processes and Simulation II, Spring 2013
Time and place: 11:50--12:40 MWF in JWB 208.
Instructor: S. Ethier (Prof.), JWB 119, 581-6148, ethier@math.utah.edu. Office hours
are 2:00--2:50 MWF. Other times are available by
appointment.
Text: Introduction to Stochastic Processes by Gregory F. Lawler (2nd ed., 2006).
Prerequisite: Math 5040 or knowledge of Markov chains and simulation.
Topics covered: We will cover martingales, renewal processes, reversible Markov chains, Brownian motion, and stochastic integration.
Grades: There will be a midterm exam around the 7th week. There will be a final exam at the scheduled time. Grades will be based on homework (30%), a project (20%), midterm exam (20%), and final exam (30%).
Project: Write a paper (3-10 pages, say) on some aspect or application of stochastic processes and/or simulation. You can use material from the mathematical literature (see MathSciNet or JSTOR or arXiv or Google Scholar, for example) as long as you give proper credit to anyone whose ideas you use. But there should also be something original in your project. It could be a simulation or a computation you have carried out further than others before you. You could generalize one of the problems done in class. Let me know if you have trouble finding a topic, and I will help with that. Ideally, it should be something that interests you. Papers should be typed. You can insert handwritten equations if you don't know LaTeX. Due last day of class.
Expected learning outcomes: The student who successfully completes Math 5050 will have a working knowledge of stochastic processes and in particular will be familiar with martingales, renewal processes, reversible Markov chains, Brownian motion, and stochastic integration. Such a student will have sufficient background to apply stochastic processes in his or her own field of interest.