Abstract
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 α is ϕ(r) = rN−d/α(log log 1/r)d/α when Nα > d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d,α) strictly stable processes.
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Supported partly by the NNSF of China (Nos. 10371092, 10171015 and No. 10271027)
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Zheng, S.C., Lin, H.N. & Hu, D.H. The Exact Hausdorff Measure Function of the Level Sets of Multi–parameter Symmetric Stable Process. Acta Math Sinica 21, 1137–1148 (2005). https://doi.org/10.1007/s10114-004-0521-1
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DOI: https://doi.org/10.1007/s10114-004-0521-1