A direct construction of the Standard Brownian Motion

preprint2020arXivOpen access

Abstract

In this note, we combine the two approaches of Billingsley (1998) and Csőrgő and Révész (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.

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