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Exact Hausdorff measure for the product set of the ranges of stable component processes
Received date: 2013-04-25
Revised date: 2013-06-13
Online published: 2014-07-15
Let {X1(t1),t1≥0},…,{Xp(tp),tp≥0} be p independent stable component processes on Rd. We obtain the law of the iterated logarithm for the measure on the product set ∏i=1pXi[0,1]. Furthermore, by applying the density theorem, we find the exact Hausdorff measure of the product set. As a special case, we deduce the exact Hausdorff measure of the product set of graphs of p independent stable processes on Rd.
LIANG Longyue . Exact Hausdorff measure for the product set of the ranges of stable component processes[J]. Journal of University of Chinese Academy of Sciences, 2014 , 31(4) : 453 -459 . DOI: 10.7523/j.issn.2095-6134.2014.04.002
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