Best Approximation of Multidimensional Random Signals

Abstract

Let: E^m be the set of sites t = {t⁽ⁱ⁾, 1 ≤ i ≤ m} with t⁽ⁱ⁾ integers; τ, S finite, τ ⊂ S ⊂ E^m; ξ_t a random variable taking values in the measurable space (X_t,Σ_t) with probability measure $P_{{\xi}_t}$, x_t ∈ X_t, T_t ∈ Σ_t; ξ(τ) = {τ_t, t ∈ τ}, (X(τ) ,Σ (τ)) the product of (X_t,Σ_t), t ∈ τ; ξ = ξ (S), a random field with values in (X,ξ) with probability P_ξ.