具有连续参数齐次随机场的线性预测

Linear Prediction Theory of a Homogeneous Random Field with Continuous Parameters

本文研究具有连续参数齐次随机场 {x(s,t) }在不对称半平面上已观察到的预测问题 ,且建立了 {x(s,t)

Let {x(s,t)} be a homogeneous random field with continuous parameters.Generallly,linear prediction problems of a homogeneous random field with continuous parameters are as follows:let G and G′ are two dimensional Borel sets,{x(s,t)} have been observed if (s,t)∈G.But {x(s′,t′)} are unknown quantities if (s′,t′)∈G′.We want to predict {x(s′,t′),(s′,t′)∈G′} by the linear conbination of the {x(s,t),(s,t)∈G} and its limit in terms of square mean,such that its error of square mean is minimum.In this paper,following linear prediction problem is discussed:G={(s,t),-∞<s<∞,t≤0}∪{(s,τ),s≤0},G′={(s,τ),s>0}.Where τ is positive and constant.