摘要
Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.
基金
Supported by National Natural Science Foundation of China(Grant No.11971432)
Natural Science Foundation of Zhejiang Province(Grant No.LY21G010003)
Humanities and Social Sciences Foundation of the Ministry of Education(Grant No.18YJA910001)
First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)
Natural Science Foundation of Chuzhou University(Grant No.zrjz2019012)。
