ON THE HITTING PROBABILITIES OF LIMSUP RANDOM FRACTALS

Abstract

Let [Formula: see text] be a limsup random fractal with indices [Formula: see text] and [Formula: see text] on [Formula: see text]. We determine the hitting probability [Formula: see text] for any analytic set [Formula: see text] with the condition [Formula: see text], where [Formula: see text] denotes the Hausdorff dimension. This extends the correspondence of Khoshnevisan et al.1 by relaxing the condition that the probability [Formula: see text] of choosing each dyadic hyper-cube is homogeneous and [Formula: see text] exists. We also present some counterexamples to show the Hausdorff dimension in condition [Formula: see text] cannot be replaced by the packing dimension.