收稿日期: 2013-04-25
修回日期: 2013-06-13
网络出版日期: 2014-07-15
基金资助
国家自然科学基金（11171342）资助
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
设{X1（t1），t1≥0}，…，{Xp（tp），tp≥0}是取值于Rd上p个相互独立稳定分量过程，讨论乘积集∏i=1pXi[0，1]上的占时测度的重对数律，并利用密度定理得到乘积集的确切Hausdorff测度.作为特例，给出了Rd上p个相互独立的严格稳定过程图集乘积集的确切Hausdorff测度.
关键词： 稳定分量过程; 重对数律; Hausdorff测度
梁龙跃 . 稳定分量过程像集乘积集的确切Hausdorff测度[J]. 中国科学院大学学报, 2014 , 31(4) : 453 -459 . DOI: 10.7523/j.issn.2095-6134.2014.04.002
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.
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