Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing ...Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.展开更多
Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measu...Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.展开更多
The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower...The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.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 Humanities and Social Sciences Research Project of Ministry of Education(Grant No.18YJA910001)the National Natural Science Foundation of China(Grant No.11371321)the first author is also supported by the Education and Scientific Research Foundation for Young and Middle-aged teachers of Fujian Province(Grant No.B17154)
文摘Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.
基金Supported by National Natural Science Foundation of China(Grant No.11371321)
文摘Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)
文摘The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
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.
