A Series Expansion of a Certain Class of Isotropic Gaussian Random Fields with Homogeneous Increments
نویسنده
چکیده
Dzhaparidze and van Zanten (2004, 2004b) proved an explicit series expansion of the multi-parameter fractional Brownian sheet. We extend their results to a certain class of isotropic Gaussian random fields with homogeneous increments, In particular, this class contains the multi-parameter fractional Brownian motion. Let ξ(x) be a centred mean-square continuous Gaussian random field with homogeneous increments on the space R . It means that for any y ∈ R random fields ξ(x + y)− ξ(y) and ξ(x) have the same finitedimensional distributions. According to (Yaglom, 1957), the autocorrelation function R(x,y) = Eξ(x)ξ(y) has the form
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