Study on A Direct Construction of the Standard Brownian Motion

Abstract

In this note, we combine the two approaches of Billingsley (1998) and Csőrgő and Revesz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is the class of non-negative dyadic numbers. By adding the proof of Etemadi's inequality to text, it becomes self-readable and serves as an independent source for researches and professors.