Packing Dimension Results for Anisotropic Gaussian Random Fields
نویسندگان
چکیده
Let X = {X(t), t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) = ( X1(t), . . . , Xd(t) ) , ∀ t ∈ R , where X1, . . . , Xd are independent copies of a centered real-valued Gaussian random field X0. We consider the case when X0 is anisotropic and study the packing dimension of the range X(E), where E ⊆ RN is a Borel set. For this purpose we extend the original notion of packing dimension profile due to Falconer and Howroyd [11] to the anisotropic metric space (RN , ρ), where ρ(s, t) = ∑N j=1 |sj − tj | Hj and (H1, . . . , HN ) ∈ (0, 1)N is a given vector. The extended notion of packing dimension profile is of independent interest.
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