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›› 2014, Vol. 31 ›› Issue (4): 453-459.DOI: 10.7523/j.issn.2095-6134.2014.04.002

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Exact Hausdorff measure for the product set of the ranges of stable component processes

LIANG Longyue   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2013-04-25 Revised:2013-06-13 Online:2014-07-15

Abstract:

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.

Key words: stable component process, the law of the iterated logarithm, Hausdorff measure

CLC Number: