The Numerical Characteristics of the Kinetically Modelled Simple Nonstationary Random Process

Abstract

The simple nonstationary random process with the sufficiently smooth realizations is considered. On the basis of kinetic modelling, the governing parameter of the process is represented for the each realization as the function of time and parameters of the kinetic equation. According to the realizations, these parameters represent the system of random quantities. As a result, the nonstationary random process is represented by the usual function of system of limited number of random quantities. For the purpose of reliability, the numerical characteristics of this process are determined by two approximate methods: linearization of function and analysis using the hypothesis of the normal distribution of the system of random quantities. The proposed lemma along with the hypothesis of the normal distribution of the system of random quantities gives the analytical expressions for the numerical characteristics up to the correlation functions for the process and for its rate. It is noted that just the expression for the expectation value contains the variances of the random quantities. In this connection, the variance restrictions are obtained. It is shown that for the both approaches the numerical characteristics converge as the variances decrease. The suggested method is illustrated with the repeatability of the process of the biological destruction of some medicine.