Sampling-reconstruction procedures of gaussian process realizations

The statistical description of Sampling-Reconstruction Procedure (SRP) of Gaussian process realizations on the base of the conditional mean rule is described. The sampled process can be stationary or non stationary. The sample set is arbitrary both in the number and location of samples. The reconstruction procedure can be carried out with an arbitrary delay in respect to the time of the last sample. Reconstruction error functions (either for extrapolation or interpolation procedures) are characterized by conditional variance. Many examples of SRP are considered, including both sampling and reconstruction of two types of stochastic Gaussian processes. The first type is characterized by the infinite spectrum, and the second by the finite spectrum. We show that Balakrishnan's theorem is a particular case of the reconstruction algorithm discussed. The SRP with a jitter effect is also investigated.