Analysis and Applied Mathematics Seminar
Shuwen Lou
UIC
Fractal properties of rough differential equations driven by fractional Brownian motion
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.
Monday March 14, 2016 at 4:00 PM in SEO 636