| Lectures: | Mon, Wed: 1:15-2:30 PM in Physics 119 | ||||
| Prof: | Jonathan C. Mattingly ( jonm@math.duke.edu) | ||||
| Office: | Physics 279, 660-6978 | ||||
| Office Hours: | TBA | ||||
This course will be an introduction to stochastic calculus and stochastic differential equations. Though the courses will be rigorous, the choice of topics will reflect those most useful in the applications of stochastic calculus. This course should be assessable to students from a variety of backgrounds including math, statistics, physics, engineering, and finance; provided they have had some exposure to basic real analysis and partial differential equations. Exposure to measure theory will be helpful though not required. Math 241 is more than sufficient as background, though Math 203 should also give enough background. Those with concerns about there preparation should contact the instructor.
Topics will include: Brownian Motion, stochastic integration, Ito's formula, diffusions, forward/backward Kolmogorov's equations, Feynman-Kac's formula, connections with PDEs, Girsanov's theorem, and martingales. If time permits, at the end we will discuss multi-scale stochastic differential equations and limit theorems. A rough outline is available here.
Exposure to measure theory will be helpful though not required. Math 241 is more than sufficient as background, though Math 203 should also give enough background. Those with concerns about there preparation should contact the instructor.