ON THE HITTING PROBABILITIES OF LIMSUP RANDOM FRACTALS

摘要

Let A be a limsup random fractal with indices gamma(1), gamma(2) and delta on [0, 1](d). We determine the hitting probability P(A boolean AND G) for any analytic set G with the condition ((*)): dim(H) (G) > -gamma(2) + delta, where dim(H) denotes the Hausdorff dimension. This extends the correspondence of Khoshnevisan et at.(1) by relaxing the condition that the probability P-n of choosing each dyadic hyper-cube is homogeneous and lim(n ->infinity) log(2) P-n/n exists. We also present some counterexamples to show the Hausdorff dimension in condition ((*)) cannot be replaced by the packing dimension.

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