Dimension Results for Space-anisotropic Gaussian Random Fields  

作　　者：Wen Qing NI Zhen Long CHEN Wei Gang WANG 

机构地区：[1]School of Statistics and Mathematics, Zhejiang Gongshang University [2]School of Science, Jimei University

出　　处：《Acta Mathematica Sinica,English Series》2019年第3期391-406,共16页数学学报（英文版）

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)

摘　　要：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.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.

关 键 词：HAUSDORFF DIMENSION PACKING DIMENSION GAUSSIAN random field UNIFORM DIMENSION 

分 类 号：O1[理学—数学]