Study of the dynamics of multidimensional stochastic systems based on entropy modeling

A new entropy approach of modeling of dynamics of stochastic systems is described. It is based on the representation of the system in the form of a multidimensional stochastic vector. It is shown that the change in entropy of a multivariate stochastic system can be expressed in terms of dispersions and conditional correlations of a component of a random vector. This allows to reveal the cause of the change in the entropy of the system and to evaluate it quantitatively. It was found that the entropy of a stochastic system consists of two components that characterize its properties. The first component determines the limit entropy corresponding to the full independence of the elements of the system and defines the consideration of the integral object as consisting of components (additivity). The second component reflects the extent of interrelation between the elements of the system, defining the properties of the system as a whole (integrity). This approach makes it possible to use entropy models in the diagnostics and control of stochastic systems as well as efficient management. The advantages of the proposed approach include the simplicity of implementation and interpretation of the mathematical model, the universality and adaptability for stochastic systems of different nature, the possibility of its use on small samples of data. The article contains an example of the practical application of a mathematical model.