数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 969-992.doi: 10.1016/S0252-9602(11)60290-7

• 论文 • 上一篇    下一篇

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

陈振龙   

  1. College of Statistics and Mathematics, |Zhejiang Gongshang University, Hangzhou  |310018, China
  • 收稿日期:2009-05-19 修回日期:2010-03-05 出版日期:2011-05-20 发布日期:2011-05-20
  • 基金资助:

    Research supported by the Natural Science Foundation of Zhejiang Province (Y6100663).

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

 CHEN Zhen-Long   

  1. College of Statistics and Mathematics, |Zhejiang Gongshang University, Hangzhou  |310018, China
  • Received:2009-05-19 Revised:2010-03-05 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    Research supported by the Natural Science Foundation of Zhejiang Province (Y6100663).

摘要:

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by   constructing a
Cantor-type set to connect its Hausdorff dimension and capacity.

关键词: random string process, hitting probability, polar set, Hausdorff dimension

Abstract:

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by   constructing a
Cantor-type set to connect its Hausdorff dimension and capacity.

Key words: random string process, hitting probability, polar set, Hausdorff dimension

中图分类号: 

  • 60G15