Necessary Notions from the Theory of Stochastic Processes
摘要
To facilitate the reader’s understanding, we will now present the fundamental formulas of the theory of stochastic processes that are essential for the subsequent discussions. While some of these formulas are well-known, others are only found in obscure publications, and a few are being cited for the first time. Although these formulas primarily focus on the initial two moments of probability distributions, they possess a straightforward structure and content, yet their level of familiarity is not widespread. Certain formulas can be derived by considering similarity and dimensionality, thus the material presented here may offer further validation for their accuracy and applicability limits, as well as for the analysis of empirical data. The exposition will specifically address temporal processes, which pertain to processes in a one-dimensional space. The statistical theory of random vector fields was originally developed by A. M. Obukhov in the 1940s, and a comprehensive explanation can be found in volume II of the book authored by A. S. Monin and A. M. Yaglom, referred to as MY75.