Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropi...Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.展开更多
In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C...In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].展开更多
In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of...In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11971432)Natural Science Foundation of Zhejiang Province(Grant No.LY21G010003)+2 种基金Humanities and Social Sciences Foundation of the Ministry of Education(Grant No.18YJA910001)First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)Natural Science Foundation of Chuzhou University(Grant No.zrjz2019012)。
文摘Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.
基金supported by the NSFC (11701001,11626030)the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqzD2020021)the Scientific Research Project of Colleges and Universities in Anhui Province,2023。
文摘In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].
文摘In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.
