On intersections of independent anisotropic Gaussian random fields

作     者：CHEN ZhenLong XIAO YiMin 

作者机构：School of Statistics and MathematicsZhejiang Gongshang UniversityHangzhou 310018China Department of Statistics and ProbabilityMichigan State UniversityEast Lansing:MI 48824USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2012年第55卷第11期

页      面：2217-2232页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by Zhejiang Provincial Natural Science Foundation of China(Grant No. Y6100663) National Science Foundation of US (Grant No. DMS-1006903) 

主　　题：高斯噪声 各向异性 交叉点 随机 Riesz平均 度量空间 样本路径 充分条件 

摘      要：Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,*** of intersections of the sample paths of X H and X K is *** generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where  is a metric defined in terms of H and *** results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.