Hausdorff Measure of Space Anisotropic Gaussian Processes with Non-stationary Increments  

作　　者：Jun WANG Zhen-long CHEN Wei-jie YUAN Guang-jun SHEN 

机构地区：[1]School of Mathematics and Physics,Anhui Polytechnic University,Wuhu 241000,China [2]School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China [3]Department of Mathematics,Anhui Normal University,Wuhu 241000,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第1期114-132,共19页应用数学学报(英文版)

基　　金：partially supported by National Natural Science Foundation of China(12371150,12071003);Natural Science Foundation of Anhui Polytechnic University(2022AH050955,2022YQQ025,Xjky2022163);Zhejiang Province Philosophy and Social Science Planning Routine Subject(24NDJC131YB).

摘　　要：Let X={X(t),t∈R+} be a centered space anisotropic Gaussian process values in R^(d) with non-stationary increments,whose components are independent but may not be identically distributed.Under certain conditions,then almost surely c_(1)≤ϕ-m(X([0,1]))≤c_(2),where ϕ denotes the exact Hausdorff measure associated with function ϕ(s)=s1/α_(k)+Σ_(i=1)k(1-αi/αk)log log 1/s for some 1≤k≤d,(α_(1),…,α_(d))∈(0,1]^(d).We also obtain the exact Hausdorff measure of the graph of X on[0,1].

关 键 词：Hausdorff measure self-similar Gaussian processes non-stationary increment Lamperti theorem 

分 类 号：O211.6[理学—概率论与数理统计]