Polar Functions and Intersections of the Random String Processes  

作　　者：Zhen Long CHEN 

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

出　　处：《Acta Mathematica Sinica,English Series》2012年第10期2067-2088,共22页数学学报（英文版）

基　　金：Supported by Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100663)

摘　　要：Let {us （x） ： s 〉 0, x ∈ JR} be a random string taking values in ]Rd. The main goal of this paper is to discuss the characteristics of the polar functions of {us （x） ： s ≥ 0, x ∈ JR}. The relationship between a class of continuous functions satisfying the HSlder condition and a class of polar-functions of {us（x） ： s 〉 0, x ∈ R} is presented. The Hausdorff and packing dimensions of the set that the string intersects a given non-polar continuous function are determined. The upper and lower bounds are obtained for the probability that the string intersects a given function in terms of respectively Hausdorff measure and capacity.Let {us （x） ： s 〉 0, x ∈ JR} be a random string taking values in ]Rd. The main goal of this paper is to discuss the characteristics of the polar functions of {us （x） ： s ≥ 0, x ∈ JR}. The relationship between a class of continuous functions satisfying the HSlder condition and a class of polar-functions of {us（x） ： s 〉 0, x ∈ R} is presented. The Hausdorff and packing dimensions of the set that the string intersects a given non-polar continuous function are determined. The upper and lower bounds are obtained for the probability that the string intersects a given function in terms of respectively Hausdorff measure and capacity.

关 键 词：Random string process stationary pinned string polar function Hausdorff dimension packing dimension capacity 

分 类 号：O174.12[理学—数学] TP312[理学—基础数学]