Spectral Contributions of Sections of the Power-Law Structure Function of Random Processes with Stationary Increments: Part 1—The Exponent is Less than Unity

Abstract

The frequency dependences of the spectral contributions of the initial, central, and “finite” sections of a power-law structure function (with the exponent less than unity) into the spectral density (SD) of a random process with stationary increments are considered. They are shown to be much more complicated than the strictly positive monotonic power-law frequency dependences of the initial SD. The latter agrees only with the behavior of the spectral contribution of the initial section of the structure function under study. The analytical approximation dependences of the frequency dependences of all these spectral contributions are derived and analyzed. They are recommended for wide practical use.