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 condition...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.展开更多
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 betwee...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.展开更多
基金supported by the Natural Science Foundation of Zhejiang Province(Y6100663)
文摘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.
基金Supported by Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100663)
文摘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.
