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Erschienen in:
2017 | OriginalPaper | Buchkapitel
4. Dependence of the Statistical Stability of a Stochastic Process on Its Spectrum-Correlation Characteristics
verfasst von : Igor I. Gorban
Erschienen in: The Statistical Stability Phenomenon
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Abstract
The Wiener–Khinchin transformation is examined. It is noted that there are stochastic processes which do not simultaneously have a correlation function that is typical for a stationary process, and a power spectral density. We determine the dependence of the statistical stability on the power spectral density of the process and investigate the statistical stability of a process for which the power spectral density is described by a power function. Results are obtained for continuous and discrete processes. We then present simulation results which confirm the correctness of the formulas describing the dependence of the statistical instability parameters on the power spectral density of the process. The dependence of the statistical stability of a process on its correlation characteristics is analyzed. The statistical stability of low frequency and narrowband stochastic processes is investigated.