Special Lecture
Packing dimension and packing measure were introduced by Tricot (1982), Taylor and Tricot (1985) in the Euclidean space as dual concepts to Hausdorff dimension and Hausdorff measure. Many authors have applied packing dimension and packing measure to study fractal properties of the sample paths of stochastic processes such as Brownian motion, stable L\'evy processes and fractional Brownian motion. In this talk, I will present some recent packing dimension results for random fractals related to Brownian motion and fractional Brownian motion. These results show that, on one hand, many Hausdorff dimension results such as the Hausdorff dimensions of the image set and the set of fast points of Brownian motion have no direct analogue for the packing dimension; and, on the other hand, even in problems where only Hausdorff dimension is concerned, packing dimension could be needed to give a complete solution.