Math 247A (Driver, Winter 2009) Topics in Real Analysis
Rough Path Analysis
Office Hours: TBA.
Meeting times: Lectures are on MWF 11:00a - 11:50a in AP&M B412.
Textbook: There is no official text book for this course. However,
there will likely be posted lecture notes on the course web-site. Other
references will be supplied as the course progresses.
Course Description: This course will be concerned with Terry Lyons’ theory which is called Rough Path Analysis. The theory is devoted to solving ordinary differential equations driven by nowhere differentiable paths. The typical equation is of the form;
dXt = A(Xt)dBt with X0 = x0 .
In this equation Bt is assumed to be a rough path with infinite variation. One of the motivations of this theory is to give a deterministic interpretation of stochastic differential equations where the typical choice for Bt is a Brownian motion. (The notion of Brownian motion is not a prerequisite for this course.) In the case of Brownian motion, Bt has infinite variation and hence the classical Stieltjes integration theory does not apply here. Nevertheless, building on the work of Young, Chen and others, Terry Lyons has developed techniques to handle such rough equations. In order to make this theory work, one must “augment” the driving noise, Bt by its “Levy area” process. The goal of this course will be to describe this theory and give some applications of it to stochastic differential equations.
List of Possible Topics
A Few Suggested References
References 1. and 3. may be acquired via MathSciNet through your UCSD account.
Last modified on Monday, 29 December 2008 12:01 PM.