Brownian motion of molecules: the classical theory

TL;DR

This paper reviews classical Brownian motion theory, introduces a new derivation method for Fokker-Planck equations from stochastic differential equations, and confirms white noise's Gaussian nature via the central limit theorem.

Contribution

It presents a novel approach to derive Fokker-Planck equations and provides a rigorous proof of white noise's Gaussian property.

Findings

New derivation method for Fokker-Planck equations

White noise proven Gaussian via central limit theorem

Clarification of classical Brownian motion theory

Abstract

A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian.