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MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS
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作者 陈振龙 苑伟杰 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期275-294,共20页
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... 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. 展开更多
关键词 anisotropic Gaussian field multiple intersections Hausdorff measure capacity
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The Study of Fuzzy Line Control for Multiple Intersections
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作者 Mingqing Jiang Zhongyi Zhang +1 位作者 Zhong Gui Pigang Chen 《Chinese Business Review》 2005年第2期56-59,共4页
The line control for multiple intersections is a hot spot in the area of transportation. According to the principle of system analysis and coordination, a method about fuzzy line control for multiple intersections is ... The line control for multiple intersections is a hot spot in the area of transportation. According to the principle of system analysis and coordination, a method about fuzzy line control for multiple intersections is proposed. The system is made of two control units, one is the basic control unit for every single intersection, and the other is used for the function of coordination. 展开更多
关键词 fuzzy line control system analysis multiple intersections
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HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS 被引量:1
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作者 Jun WANG Zhenlong CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期653-670,共18页
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 ... 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. 展开更多
关键词 Hitting probability multiple intersection anisotropic random field capacity Hausdorff dimension stochastic fractional heat equations
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