Title: Random moves equation Kolmogorov-1934. A unified approach for description of statistical phenomena of nature Show Chinese title

Title: 随机移动方程柯尔莫哥洛夫-1934。 自然统计现象的统一描述方法

Abstract: The paper by A.N. Kolmogorov 1934 "Random Moves", hereinafter ANK34, uses a Fokker-Planck-type equation for a 6-dimensional vector with a total rather than a partial derivative with respect to time, and with a Laplacian in the space of velocities. This equation is obtained by specifying the accelerations of the particles of the ensemble by Markov processes. The fundamental solution was used by A M Obukhov in 1958 to describe a turbulent flow in the inertial interval. Already recently it was noticed that the Fokker-Planck-type equation written by Kolmogorov contains a description of the statistics of other random natural processes, earthquakes, sea waves, and others. This theory, containing the results of 1941, paved the way for more complex random systems containing enough parameters to form an external similarity parameter. This leads to a change in the characteristics of a random process, for example, to a change in the slope of the time spectrum, as in the case of earthquakes and in a number of other processes (sea waves, cosmic ray energy spectrum, flood zones during floods, etc.). A review of specific random processes studied experimentally provides a methodology for how to proceed when comparing experimental data with the ANK34 theory. Thus, empirical data illustrate the validity of the fundamental laws of probability theory. Show Chinese abstract

Abstract: 由A.N.柯尔莫哥洛夫于1934年撰写的论文“随机运动”，以下简称ANK34，使用了一个6维向量的Fokker-Planck型方程，该方程相对于时间使用的是总导数而非偏导数，并在速度空间中使用拉普拉斯算子。该方程是通过用马尔可夫过程指定系综中粒子的加速度而得到的。A M Obukhov在1958年利用基本解来描述惯性区间内的湍流。最近人们注意到，柯尔莫哥洛夫写出的Fokker-Planck型方程包含对其他随机自然过程（如地震、海浪等）统计特性的描述。该理论包含了1941年的结果，为更复杂的随机系统铺平了道路，这些系统包含足够的参数以形成外部相似性参数。这导致了随机过程的特征发生变化，例如时间谱的斜率变化，如地震及其他一些过程（海浪、宇宙射线能量谱、洪水期间的洪水区等）。对实验研究的具体随机过程的综述提供了一种方法论，说明在将实验数据与ANK34理论进行比较时应如何进行。因此，实证数据展示了概率论基本定律的有效性。