Abstract: The survey of author’s researches devoted to disturbance of statistical stability of physical quantities and processes is presented. Concepts of statistical stability of random sequences and random processes are formalized. Parameters characterizing their statistical stability in finite observation interval are proposed. It is found that statistical unstable processes are especial class of non-stationary processes. Statistical stability disturbance can be explained by low frequency cyclical fluctuations of expectation. It has been researched statistical stability of a number of physical quantities and processes, in particular line voltage, height of sea waves and their periods, Earth magnetic field fluctuation, and currency rate. It has been found that for all researched quantities and processes, there is statistical stability disturbance on large observation intervals. Obtained results corroborate the hypotheses that are in base of new physico-mathematical theory of hyper-random phenomena: real physical events, quantities, processes, and fields are not statistical stabile and they can be adequately described by hyper-random models taking into consideration their statistical instability.

Keywords: statistical instability, theory of hyper-random phenomena, uncertainty, probability.

ACM Classification Keywords: G.3 Probability and Statistics

Link:

DISTURBANCE OF STATISTICAL STABILITY

Igor Gorban

http://foibg.com/ibs_isc/ibs-19/ibs-19-p50.pdf