Acta mathematica scientia, Series B >
FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES
Received date: 2009-05-19
Revised date: 2010-03-05
Online published: 2011-05-20
Supported by
Research supported by the Natural Science Foundation of Zhejiang Province (Y6100663).
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
CHEN Zhen-Long . FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 969 -992 . DOI: 10.1016/S0252-9602(11)60290-7
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