MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS  

作　　者：陈振龙 苑伟杰 Zhenlong CHEN;Weijie YUAN(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou,310018,China)

机构地区：[1]School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou,310018,China

出　　处：《Acta Mathematica Scientia》2024年第1期275-294,共20页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(12371150,11971432);the Natural Science Foundation of Zhejiang Province(LY21G010003);the Management Project of"Digital+"Discipline Construction of Zhejiang Gongshang University(SZJ2022A012,SZJ2022B017);the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics);the Scientific Research Projects of Universities in Anhui Province(2022AH050955)。

摘　　要：Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

关 键 词：anisotropic Gaussian field multiple intersections Hausdorff measure capacity 

分 类 号：O212[理学—概率论与数理统计]