Non uniform sampling and reconstruction of stochastic processes with the limited number of samples

The statistical description of the Sampling - Reconstruction Procedure (SRP) of various types of stochastic processes is given on the basis of the classical conditional mean rule which provides the minimum reconstruction error. We consider the SRP description taking into account 1) probability density function (pdf) of the sampling process and 2) the limited number of samples. Many known publications do not use these circumstances in the SRP analysis. We use the different types of the sampling processes: Gaussian with various covariance functions; non Gaussian processes of common types (for example, Rayleigh process); non Gaussian processes on the output of non linear converters (polynomial, piece-linear, exponential). New aspects of the SRP of Markovian processes with jumps are discussed also. This approach provides a possibility to investigate some new aspects of non uniform SRP: the sampled process can be stationary and non stationary; the samples with jitter are described by some new models: particularly, the jitter pdf is the Beta distribution; any samples can have their own jitter, others can have not jitter; the jitter effect can have stationary and non stationary character; the jitter effect can be independent or dependent statistically in some neighbour samples. All of the mentioned problems are shortly considered in this author's publications review.