Sampling-Reconstruction Procedure of Gaussian Processes With Jitter Characterized by the Beta Distribution

The sampling-reconstruction procedure of different Gaussian processes with jitter and with a limited number of samples is investigated. We suggest a new model for the jitter effect; this is a continuous random variable with beta distribution. In this paper, the jitters of samples are assumed to be independent. The conditional mean rule is applied in order to describe the reconstruction procedure. We use multidimensional expressions of conditional expectation and conditional variance of Gaussian processes, and then, we carry out the operation of the statistical average of random times with respect to the corresponding types of beta distribution. The applied method provides a possibility of considering the variant when each sample has its own type of jitter probability density function. In particular, one or more samples can lack jitter. Error reconstruction functions and basic functions are investigated in detail in many examples.