SOME DIMENSION RESULTS FOR SUPER-BROWNIAN MOTION

The Dawson-Watanabe super-Brownian motion has been intensively studied in the last few years. In particular, there has been much work concerning the Hausdorff dimension of certain remarkable sets related to super-Brownian motion. We contribute to this study in the following way. Let (Y-t)(t greater than or equal to 0) be a super-Brownian motion on IR(d) (d greater than or equal to 2) and H be a Borel subset of IR(d). We determine the Hausdorff Dimension of {t greater than or equal to 0; Supp Y-t boolean AND H not equal 0}, improving and generalizing a result of Krone. We also obtain a new proof of a result of Tribe which gives, when d greater than or equal to 4, the Hausdorff dimension of boolean OR(t is an element of B) Supp Y-t as a function of the dimension of B.