A noising method for the identification of the stochastic structure of information flows

Abstract

The paper demonstrates a way for application of a methodology for the stochastic analysis of random processes based on the method of moving separation of finite normal mixtures to analyze the non-negative time series. We suggest to noise the initial data by adding i.i.d. normal random variables with known parameters. Then the one-dimensional distributions of observed processes are approximated by finite location-scale mixtures of normal distributions. The finite normal mixtures are convenient approximations to general location-scale normal mixtures or normal variance-mean mixtures which are limit laws for the distributions of sums of a random number of independent random variables or non-homogeneous and non-stationary random walks and hence, are reasonable asymptotic approximations to the statistical regularities in observed real processes. This approach allows to analyze the regularities in the variation of the parameters and capturing the low-term variability in the case of complex internal structure of data. An implementation of the methodology is shown by the examples of the intensity for the simulated information system.