O Movimento Browniano como Rough Path

Abstract

In this paper we will present the Brownian Motion from the point of view of the Rough Path theory, an approach developed by Terry Lyons in the 1990s. This theory offers a convenient alternative to the Itô stochastic calculation in the study of stochastic differential equations. As prerequisites, we will build the classic Brownian Movement using the Daniell-Kolmogorov Extension Theorem and introduce the concepts of Itô and Stratonovitch integrals.