Probability distributions over energy and areas in processes described by Kolmogorov's 1934 random motion equation

The Kolmogorov equation is described in detail in the paper by G.S. Golitsyn [UFN 194 86 (2024); Phys. Usp. 67 80 (2024)], which is a summary of the book by G.S. Golitsyn, Probability structures of the macrocosm: earthquakes, hurricanes, floods (Moscow: Fizmatlit, 2022), but insufficient attention is paid to probability distributions, integral and differential, for the processes described by this equation. The integral distribution for cosmic rays is derived only by the method of similarity and dimensionality, and the distribution of horizontal lengths L of clouds and their perimeters together with the ratio of the cloud perimeter to its size are not explained at all. Here, these shortcomings are corrected, and the results and methods can be useful for other purposes.