HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS  

作　　者：Jun WANG Zhenlong CHEN 王军;陈振龙(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;School of Mathematics and Finance,Chuzhou University,Chuzhou 239000,China)

机构地区：[1]School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China [2]School of Mathematics and Finance,Chuzhou University,Chuzhou 239000,China

出　　处：《Acta Mathematica Scientia》2022年第2期653-670,共18页数学物理学报（B辑英文版）

基　　金：supported by National NaturalScience Foundation of China(11971432);Natural Science Foundation of Zhejiang Province(LY21G010003);First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics);the Natural Science Foundation of Chuzhou University(zrjz2019012)。

摘　　要：Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

关 键 词：Hitting probability multiple intersection anisotropic random field capacity Hausdorff dimension stochastic fractional heat equations 

分 类 号：O211.6[理学—概率论与数理统计]