Mathematical models and solution of problems of the transfer theory in technical systems based on the problem of filtration of the Poisson process

In this paper the problem of the filtration of a Poisson random process is solved. The theory of filtration has a rich history, but in recent decades it has taken an important place in the framework of cybernetics and engineering. The requirements of modern production and the implementation of complex control and communication systems determine the development of filtration theory methods. Much attention is paid to the formal mathematical aspects of the problem. An analytical solution of the filtration problem is constructed by the authors of the paper, the suggested approach helps to reduce the solution of the problem to the solution of a system of ordinary differential equations of the first order, and the solutions of differential equations give the desired quantities. Thus, the method for solving the problem of filtration is simplified. The proposed approach can be used in the complex engineering systems' management, for example, when proceeding data from different sensors.