Vladimir Kazakov

One-dimensional kinetic equations for non-Markovian processes and statistical analysis problems of systems driven by the asymmetrical binary Markovian process

Abstract The problem of the number of terms in the one-dimensional kinetic equation for non-Markovian processes is discussed. The comparison of solutions obtained by different kinds of kinetic equations is given. The derivation of the kinetic coefficients, when the system is driven by the asymmetrical binary Markovian process, is presented. Some examples are considered.

Statistical analysis of linear dynamic systems driven by the binary Markovian noise on the basis of the kinetic equations for non-Markovian stochastic processes

Abstract A new set of kinetic equations for non-Markovian processes is applied to the statistical description of linear dynamic systems. The expressions for multidimensional kinetic coefficients are presented. As a particular case, the binary Markovian input noise is considered. The problem of the output probability density function definition is solved for a first-order linear dynamic system. Then, the second-order linear filters are investigated. Two-dimensional kinetic equation solutions for the output probability density functions are ibtained by a numerical method in the steady-state case.

Sampling-Reconstruction Procedures of a realization of Gaussian processes with limited spectrum and with an arbitrary number of samples

The basic functions and the error reconstruction functions for the Sampling -Reconstruction Procedure of Gaussian process realizations with limited spectrum are investigated. Numbers of samples and sampling intervals are arbitrary.

Reconstruction Error Estimation of Gaussian Markov Processes with Jitter

The reconstruction error estimation of the Gaussian Markov process in the presence of jitter is investigated in this paper, taking into account mainly two samples in the analysis. Two different situations are considered. In the first situation, the position of the first sample does not have jitter, but it exists in the second sample. In the second condition, the two samples have the presence of jitter. The probability density functions of jitter are represented by the uniform and the Erlang distributions. The results are obtained by applying statistical averaging to the conditional mean rule with respect to the random variable of jitter. This rule defines the conditional variance function as reconstruction error function, which allows us to determine the reconstruction error of the Gaussian Markov process on the whole time domain.

Maximum Error Estimation of Gaussian Processes in the Sampling-Reconstruction Procedure

The Sampling-Reconstruction Procedure (SRP) of Gaussian processes is investigated in this paper on the basis of the conditional mean rule. The main advantage of this methodology is that it can estimate the reconstruction error on the whole time domain, so we have the possibility to evaluate this error in any point of interest of the analyzed process. The most important points are them, where maximum levels of error are produced. Considering the above, our essential necessity is to estimate these maxima and get an easier formula in order to make a faster error evaluation with a specific sampling interval for a singular application. Initially, the analysis is performed for two Gaussian processes: one with Markovian characteristics and other with non-Markovian properties.

Error Functions of Gaussian Fields Using Radial and Spiral Sampling

The purpose of this paper is to present two different spatial sample configurations in order to measure the error function of a given Gaussian random field. This Gaussian field is described by some two-dimensional covariance functions. We found these functions at the output of RC circuits in series. For this study we used the Sampling-Reconstruction Procedure (SRP) based on the conditional mean rule. Moreover we changed the covariance function, the quantity of samples and the distance between them. The results in this study demonstrate how all the above factors influence the error functions.

Interpolation algorithms of the non gaussian process at the output of the non linear non inertial converter

The sampling - reconstruction procedure (SRP) of a non Gaussian process at the output of the non linear non inertial converter driven by Gaussian process is considered. The type of the converter is exponential. The principal SRP characteristics (the reconstruction function and the error reconstruction function) are investigated for two different reconstruction algorithms. The first algorithm is based on the conditional mean rule. It provides the optimal the reconstruction function and the minimum of the error reconstruction function. The second algorithm is connected with the formulas for the Gaussian processes. This algorithm is no optimal. There is a comparison between both variants.

Sampling-reconstruction procedure of Gaussian processes with the mutual statistical connection between all couples of samples

This paper is devoted to the special statistical problem of the time synchronization in many modern digital systems. We investigate the Sampling-Reconstruction Procedure (SRP) of Gaussian processes when the instant times of samples are randomly changed. This effect is known as jitter. We restrict our interest to the joint jitter of any two samples. It means that the jitter effect is described by a two-dimensional probability density function (pdf). Two different pdf are used in this paper: Gaussian and the distribution obtained by McFadden. We get the error reconstruction functions for both samples. The influence of different parameters on the error reconstruction functions is investigated in detail. Some examples are presented and the results are compared when the parameter of the two jitter distributions are the same.