**Authors:** Igor I. Gorban

**Keywords:** Phenomenon of statistical stability; Probability
theory; Theory of hyper-random phenomena; Physical process;
Violation of convergence.

### Abstract

We give the survey of the researches dedicated to the statisti-
cal stability phenomenon and the physical-mathematical theory
of hyper-random phenomena that takes into account the viola-
tion of statistical stability. It is presented the study technique
of statistical stability, the results of the theoretical and experi-
mental investigations of statistical stability of various processes,
the mathematical apparatus of the theory of hyper-random phe-
nomena, the particularities of mathematical statistics of hyper-
random variables (including ones connected with the law of large
numbers and the central limit theorem), and the explanation why
the accuracy of actual measurements is limited. The description
is constructed on the comparison of the theory of hyper-random
phenomena with the probability theory.

The Institute of Mathematical Machines and Systems Problem,

National academy of sciences of Ukraine,

Glushkova ave., 42, Kiev, Ukraine, 03680

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