FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES  

作　　者：陈振龙 

机构地区：[1]College of Statistics and Mathematics Zhejiang Gongshang University

出　　处：《Acta Mathematica Scientia》2011年第3期969-992,共24页数学物理学报（B辑英文版）

基　　金：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.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 

分 类 号：O211.6[理学—概率论与数理统计]