Uma Simulação computacional do passeio aleatório simples

Abstract

In 1828 it was observed a phenomenon under a microscope in which visualized tiny pollen grains dipped into a liquid at rest that move up at random drawing a disorderly movement. The point was to understand this movement. After about 80 years, Einstein (1905) developed a mathematical formulation to explain this phenomenon, called as Brown motion, increasingly theory developed in many areas, including recently on computational modeling. The goal is to score the basic assumptions inherent in the simple random walk considering experiments with and without boundary value problem for better understanding the use of algorithms applied to computational problems. The tools needed for applying simulation models of simple random walk in the first three dimensions of space were spelled out. The interest was directed as much to the simple random walk as to possible applications for the issue of the ruin of the player and the spread of viruses in computers network. Random walk algorithms simple one-dimensional without and with boundary value problem on the platform R were developed. At the same way, they were implemented for the two-dimensional and three-dimensional spaces, enabling future applications to the problem of the spread of viruses in computers network and as motivation to study the heat equation, although it requires a greater foundation in concepts of Physics and Probability to continue such application