Abstract: Stochastic differential equations driven by fractional Brownian motions have been introduced to model random evolution phenomena whose noise has long range dependence, and have found successful applications in biotechnology and biophysics. Fox example, it is used to model the sub diffusion of electrons within a protein molecule.



In this talk, we survey some of our results on sample path properties of SDEs driven by fractional Brownian motions, including hitting properties, Hausdorff dimension of sample paths and level sets, and existence and regularity of local times.