具有連续参数的齐次随机場的线性内插

The Interpolation of Homogeneous Radom field with Continuous Parameters

在这篇文章中討論了在平面上的齐次随机場——两元平稳随机函数的綫性内插問題。过渡到n元平稳随机函数不会引起任何原則上的困难。 設{x(s,t)}为一具有連续参数的齐次随机場,其中s,t为实数。如所周知。

Let {x(s, t)} be a homogeneous radom field with continuous parametes. In the present paper we obtain the following main reasult: Theorem 1: In the homogenous radom field {x(s,t)} has been observed at the lattice points, then interpolator (s, t) of (s, t) (s≠m, t≠n) is (s,t)=integral from -∞ to ∞ integral from -∞ to ∞ e^i(sλ+tμ)dF_1(λ,μ)/dF_2(λ,μ) d z_x(λ,μ), and the error interpolation is σ_(s,t)~2=integral from -∞ to ∞ integral from -∞ to ∞|1-dF_1(λ,μ)/dF_2(λ,μ)|~2F_x(λ,μ) where F_1(λ,μ)=sum from l=-∞ to ∞ sum from j=-∞ to ∞[F_x(λ+2lπ, μ+2jπ)—F_x(2lπ,2jπ)]e^(2πi(ls+J^t) F_2(λ,μ)=sum from l=-∞ to ∞ sum from j=-∞ to ∞[F_x(λ+2lπ,μ+2jπ)—F_x(lπ,2jπ)].