The Exact Hausdorff Measure Function of the Level Sets of Multiparameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N.parameter R d.valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N.parameter R d.valued stable processes. We show that the exact Hausdorff measure function of level sets of N.parameter R d.valued symmetric stable processes of index . is .(r) = rN.d/.(log log 1/r)d/. when N. > d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d,.) strictly stable processes.