Sampling-Reconstruction Procedure with a Limited Number of Samples of Stochastic Processes at Random Times

The review of author’s publications is presented. All papers are based on the same methodological approach: the statistical description of the Sampling Reconstruction Procedure (SRP) is given on the basis of the classical conditional mean rule which provides the minimum reconstruction error. There are two cases of non uniform sampling: the sample location is arbitrary and known and the location of samples is unknown and is described by probability density function (pdf). There are some principal distinctions between reviewed papers and known publications: the number of samples is limited and arbitrary, the pdf of sampled processes is taken into account, the sampled process can be stationary and non stationary, the samples with jitter are described by some new models: the jitter pdf is the Beta distribution, any samples can have their own jitter, other can have not jitter, the jitter effect can have stationary and non stationary character. New aspects of the SRP of Markovian processes with jumps are discussed also. Key-Words: Random sampling, Optimal reconstruction, Stochastic processes.