Theory of Brownian Motion and its Applications in Selected Examples

Random walk is the basic concept in mathematics. Brownian motion is one of the most popular application. The core of the Brownian motion is the continuous path for small particles. After being developed by Wiener, it is used in many other studies, including biology, chemistry, and economics. Brownian motion is contemporarily used for predicting possible path. For animals scientists can know the probable range of activities for animals in order to keep people from bothering them and keep them out of danger. For chemical reactions, it is easy to predict every tiny particle about their movement so that people can directly understand the core of the reaction and one can predict the speed and the phenomenon of the reaction. For economics, economists can use the Brownian motion to calculate the probability for stock to up or down. This paper aims to present the theory of Brownian motion and illustrate the applications. This allows people to better choose the time to buy and sell in order to get the highest profit, and makes the economic market more controllable.