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中国科学院大学学报 ›› 2014, Vol. 31 ›› Issue (5): 577-585.DOI: 10.7523/j.issn.2095-6134.2014.05.001

• 数学 •    下一篇

稳定分量过程像集乘积集的确切填充测度

梁龙跃   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2013-04-30 修回日期:2013-11-25 发布日期:2014-09-15
  • 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 packing 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:2013-04-30 Revised:2013-11-25 Published:2014-09-15

摘要:

设{X1t1),t1≥0},…,{Xptp),tp≥0} 是取值于 Rdp 个相互独立的稳定分量过程,讨论乘积集 ∏i=1p Xi[0,1] 上占时测度的重对数律,并利用密度定理得到乘积集的确切填充测度.作为特例,给出R dp个相互独立的严格稳定过程像集与图集乘积集的确切填充测度.

关键词: 稳定分量过程, 重对数律, 填充测度

Abstract:

Let {X1(t1),t1≥0}, …,{Xp(tp),tp≥0} be p independent stable component processes in Rd. We obtain the law of the iterated logarithm for the measure on the product set ∏ i=1pXi[0,1]. By applying the density theorem, we derive the exact packing measure of the product set. As a special case, we deduce the exact packing measure of the product set of ranges and graphs for p independent stable processes in Rd.

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

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