(Universidade Federal do Espírito Santo, 2014-12-12) Duque, Oscar Mario Londoño; Valentim, Fábio Júlio da Silva; Cansino, Hugo Alexander de La Cruz; Cortez, Milton Edwin Cobo
This text has as main objective to study an introductory way Brownian motion. We intend to present some properties of their trajectories, in particular, addressing questions of continuity, differentiability and recurrence. Furthermore, Brownian motion identified as an example of different classes of stochastic processes, for example, as a Markov process, Gaussian, Lévy and martingale. Finalized with construction of some processes from Brownian motion.