Filtering and Estimation of the Mean

Abstract

Let us consider a random process of the form

$$ \xi (t) = \theta (t) + \Delta (t), \,\,\,\,\,\,\,t \in T, $$

((1.1))

where θ (t), t ∈ T, is an unknown deterministic function from a given class Θ and Δ(t), t ∈ T, is a Gaussian stationary process with zero mean and correlation function B(t).