Kaula's rule is a consequence of probability laws by A. N. Kolmogorov and his school

TL;DR

This paper discusses how Kaula's rule emerges from fundamental probability laws, based on A. N. Kolmogorov's early 1930s work on analytical methods in probability theory and Markov processes.

Contribution

It links Kaula's rule to probability laws through Kolmogorov's foundational work on Markov processes and their evolution equations.

Findings

Kaula's rule is derived from probability laws.

Kolmogorov's work on Markov processes underpins Kaula's rule.

The paper connects early 20th-century probability theory to geophysical observations.

Abstract

At the beginning of 1930-s A. N. Kolmogorov has published three papers on analytical methods for the probability theory. The two-page work had the essence of the approach started by A. Einstein and developed further by Fokker and Planck. He proposed a fundamental solution for evolution description of the 6D vector of the probability distribution at the Markov character of action which in modern terms is usually called as time delta-correlated acceleration. This is an approximation of processes when correlation time of random forces is much smaller than the reaction time of the system in consideration.