Examples
It is the goal of this section to simply give you a feeling for the types of areas where the Brownian motion function is used. It should be noted that there is a large amount of mathematical complexity behind the actual expression of the Brownian motion function, and its application to real world problems. However, without having any understanding of the function except for its properties and its graphs, you can still get an appreciation of its usefulness.
1. Stock Market - Here it is applied in order to gain an understanding of how a stock price will vary over a certain period time.
3. Scheduling Problems - Here it is used in computer networks or neural networks in order to determine the optimal sequence of handling tasks. Under this application it may also be applied to the manufacturing industry, in order to help production become more efficient.
4. Medical Imaging - In this situation the Brownian motion function is used to help in image classification. In this sense it is used to help predict the seemingly random shape along the image boundary.
5. Estimation of Extreme Weather - Here we use the Brownian motion function in attempts to estimate areas that had received extreme weather, such as flooding and drought, centuries ago. It may also be used to predict future events of extreme weather.
So it is clear, just from these few examples, that the Brownian motion function has applications over a wide range of areas from business to computer networks to meteorology!
Further explanations of Brownian motion applications can by found in two articles by Y.K. Lee 7.