Some Aspects of the Central Limit Theorem and Related Topics

Abstract

Very often the observation of natural phenomena leads to an average trend with fluctuations around it. One of the most well known example is the observation by Brown and others of a pollen particle in water. The particle is subject to many collisions with water molecules and an average behaviour follows by the law of large numbers. Here the average velocity of the particle is zero, and the particle should stay at rest. However the observation reveals an erratic motion known as Brownian motion. The goal of the central limit theorem (abbreviated below as CLT) and the related results is to study these fluctuations around the average trend.