Abstract
Here we formalize the notion of statistical stability of a process. The parameters of statistical instability with respect to the average and with respect to the standard deviation are investigated. Measurement units are proposed for the statistical instability parameters. We specify the concept of an interval of statistical stability of a process. The dependencies of the statistical stability of a process on its power spectral density and its correlation characteristics are established. We then consider various processes described by a power function of the power spectral density and investigate the statistical stability of such processes. For narrowband processes, we present the investigation results of statistical stability violations. Statistically unstable stationary processes are considered. We present experimental results for the statistical stability of a number of actual processes of different physical kinds.
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Notes
- 1.
Along with the concept of statistical stability in the broad sense, there is a concept of statistical stability in the narrow sense (Gorban 2014). It is not used in our description, so we do not dwell on it.
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Gorban, I.I. (2018). Methodology and Results from Investigation of the Statistical Stability of Processes. In: Randomness and Hyper-randomness. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-60780-1_6
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DOI: https://doi.org/10.1007/978-3-319-60780-1_6
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