The principal investigator will continue his work relating various measures of dimension (e.g. Hausdorff and packing measures) to fractal objects of probabilistic origin (specific stochastic processes). The investigator wishes to extend the theory in two directions: firstly, to subsets of the d dimensional lattice and random walks on this lattice; and secondly, to the study of the sample paths of measure valued diffusions. Since recent developments in physics in which ideas involving fractals and their dimension play a prominent role, the work could have important implications for physicists.
