Summary: Stochastic Processes: Math 229B
Spring 2004, TTh 11-12:30
Professor: MICHAEL ANSHELEVICH
Description: The course will be based primarily on Øksendal's Stochastic Differ-
ential Equations book. We will develop the basic theory of stochastic integrals.
The theory itself is quite beautiful; in addition, stochastic integration and SDEs
have found applications in statistical physics, engineering, and finance, as well as
in mathematical fields such as PDEs and differential geometry. Our goal is to build
a foundation, so that the students can then use it for the applications they need, for
example in the final project (see below).
Prerequisites: Knowledge of measure-theory based probability is essential. Since
Math 229A was taught in the fall, we will review the background (Chapter 2 of
the textbook) in the beginning of the course. For people who haven't taken Math
229A, familiarity with the notion of stochastic process and basic properties of the
Brownian motion will make the first weeks much more manageable.
Grading: based on weekly homeworks and a final project. The project may be
based on a book chapter, a paper, or contain new material, and should be on a topic
of interest to the student which is also related to the content of the course. The later
chapters of the textbook contain a number of such possible applications.
Topics to be covered: