APPROXIMATIVE ANALYSIS OF PROBABILISTIC CHARACTERISTICS OF RANDOM PROCESSES

Prokhorov Sergey Antonovich, doctor of technical sciences, professor, head of sub-department of information systems and technology, Samara State Aerospace University named after S. P. Korolev, sp@smr.ru

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The article describes the main results obtained in the field of application analysis of random processes, time series and flows of events. It highlights the issue and describes the main stages of approximative analysis of probabilistic characteristics. It briefly specifies the results obtained in the course of research works in the field of development of technology and software for automated systems of random processes application analysis, including: mathematical description, methods and algorithms of simulation of random processes, flows of events and nonuniform time series; methods and algorithms of analysis of distribution laws, characteristic functions, correlation and spectral functions, structural functions; and solution of problems of secondary processing of time series, including identification of random processes in terms of the type of functional characteristic, approximation of distribution laws, characteristic, correlation and structural functions, power spectral density, by means of parametric models, which are the functions of given type as well as the orthogonal functions of exponential type. It gives the description of functionality of the automated systems set enabling to solve different application problems of analysis of random processes and time series. The article also describes the examples of real problems which solution involved the specified methods and algorithms of application analysis of random processes: in physics, acoustics, oceanology, medicine, machine engineering and other fields where the researchers face the necessity to process random processes with various characteristics.

stochastic processes, stochastic flows, orthogonal functions, correlationspectral analysis, time series, automated systems.