Shuwen Lou : Fractal properties of rough differential equations driven by fractional Brownian motion

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

March 14, 2016, 4 p.m.

In

SEO 636

Abstract

We will introduce fractal properties of rough differential equations driven by frational Brownian motion with Hurst parameter H>1/4. We will first survey some known results on density and tail estimates of such processes. Then we will show the Hausdorff dimension of the sample paths is equal to min(d, 1/H), where d is the dimension of the process. Also we will show that with positive probability, the level sets in the form of {t: X_t=x } has Hausdorff dimension 1-dH when dH<1, and are almost surely empty otherwise.