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The paper by A.N. Kolmogorov 1934 "Random Moves", hereinafter ANK34, uses aFokker-Planck-type equation for a 6-dimensional vector with a total rather thana partial derivative with respect to time, and with a Laplacian in the space ofvelocities. This equation is obtained by specifying the accelerations of theparticles of the ensemble by Markov processes. The fundamental solution wasused by A M Obukhov in 1958 to describe a turbulent flow in the inertialinterval. Already recently it was noticed that the Fokker-Planck-type equationwritten by Kolmogorov contains a description of the statistics of other randomnatural processes, earthquakes, sea waves, and others. This theory, containingthe results of 1941, paved the way for more complex random systems containingenough parameters to form an external similarity parameter. This leads to achange in the characteristics of a random process, for example, to a change inthe slope of the time spectrum, as in the case of earthquakes and in a numberof other processes (sea waves, cosmic ray energy spectrum, flood zones duringfloods, etc.). A review of specific random processes studied experimentallyprovides a methodology for how to proceed when comparing experimental data withthe ANK34 theory. Thus, empirical data illustrate the validity of thefundamental laws of probability theory.

Random moves equation Kolmogorov-1934. A unified approach for description of statistical phenomena of nature