ABSTRACT
A two-dimensional Brownian motion is a stochastic process that keeps track of two coordinates, both of which are independent Brownian motions. The R syntax below simulates and plots one trajectory of a two-dimensional Brownian motion. A three-dimensional Brownian motion is a stochastic process that models position by three coordinates, defined by three independent Brownian motions. Animal behavior researchers use the Brownian bridge to model movements of herds as they walk on their trails during daylight time and return to their designated lodging for an overnight stay. A geometric Brownian motion is often used to model the behavior of a stock price over time. As opposed to stock and option prices that can rise indefinitely, interest rates and commodity prices move in a limited range. Investors are interested in estimating correlation between various financial investments.
