Sampling of multidimensional Gaussian processes

The case of the Sampling-Reconstruction Procedure (SRP) of stochastic process with limited number of samples is the most important variant both for theory and practice. In order to determine the optimal reconstruction function and to calculate the minimum error reconstruction function, it is necessary to apply the classical conditional mean rule. In this paper we deal with the statistical description of the SRP of multidimensional Gaussian process when the number of samples is limited. In this case we have sampling of some components of a vector Gaussian process. One can investigate the SRP of all components on the base of all sets of samples. There are two types of linear systems considerations: the first is the series system and the second is the parallel system. The output process of every filter is one component of the vector Gaussian process. The case of the series system is concerned with the linear transformations Z(t) of a given stochastic process y(t). One can see that the reconstruction algorithm based on the multidimensional presentation of the SRP provides the best results. In the same manner one can investigate the case of other linear transformations: the differentiation and the delay.