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中国科学院大学学报 ›› 2014, Vol. 31 ›› Issue (4): 453-459.DOI: 10.7523/j.issn.2095-6134.2014.04.002

• 数学 • 上一篇    下一篇

稳定分量过程像集乘积集的确切Hausdorff测度

梁龙跃   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2013-04-25 修回日期:2013-06-13 发布日期:2014-07-15
  • 通讯作者: 梁龙跃,E-mail:lianglongyue11b@mails.ucas.ac.cn
  • 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

LIANG Longyue   

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

摘要:

设{X1t1),t1≥0},…,{Xptp),tp≥0}是取值于Rdp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Rdp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

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

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