The monograph compares two approaches that describe the statistical stability phenomenon - one
proposed by the probability theory that ignores violations of statistical stability and another
proposed by the theory of hyper-random phenomena that takes these violations into account.
There are five parts. The first describes the phenomenon of statistical stability. The second
outlines the mathematical foundations of probability theory. The third develops methods for
detecting violations of statistical stability and presents the results of experimental research
on actual processes of different physical nature that demonstrate the violations of statistical
stability over broad observation intervals. The fourth part outlines the mathematical
foundations of the theory of hyper-random phenomena. The fifth part discusses the problem of
how to provide an adequate description of the world.The monograph should be interest to a wide
readership: from university students on a first course majoring in physics engineering and
mathematics to engineers post-graduate students and scientists carrying out research on the
statistical laws of natural physical phenomena developing and using statistical methods for
high-precision measurement prediction and signal processing over broad observation
intervals.To read the book it is sufficient to be familiar with a standard first university
course on mathematics.
