Math 831: Probability I
Prerequisites:
Comfort with rigorous analysis and some elementary probability are necessary. Probability theory operates in a measure-theoretic framework, so it is important to know basic measure theory. Depending on the needs of the audience, the course can start with a quick overview of the necessary measure theory.
Instructor:
Timo Seppalainen
Time and Place:
TR 11:00-12:15 Course Content:
This is the first semester of a two-semester
graduate-level introduction to probability theory and it
also serves as a stand-alone introduction to the subject.
The course will focus on discrete-time stochastic processes
and cover at least the following topics:
foundations (probability spaces and existence
of processes), independence, zero-one laws, laws of large numbers,
weak convergence and the central limit theorem,
conditional expectations and their properties, and
martingales (convergence theorem and basic properties).