This is a measure theoretic introduction to Brownian motion and stochastic calculus, followed by an introduction to other processes. In particular, we will also study stable processes (Levy processes) and fractional Brownian motion. There will be weekly homeworks, along with an in-class midterm and final. The exams will test for familiarity with concepts and definitions used in class. The homework will be half of the grade, with the exams being the other half. This is a valuable course to take if you are interested in doing research in mathematical finance or advanced stochastic processes.
We will begin the course with a brief review of the measure theory we will be using in the course, but this will be brief so students need to have had a course on measure theory such as Math 241 or Stat 205 at some point.
Karatzas and Shreve, Brownian Motion and Stochastic Calculus, 2nd Edition
The course website will use the blackboard system, found at https://courses.duke.edu.
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Last modified: 23 October 2002