Geometric Brownian motion by a different Brownian Motion—the model is called a stochastic volatility model. Geometric Brownian motion A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model. A stochastic process "S" is said to follow a GBM if it satisfies the following stochastic differential equation (SDE):
Brownian surface Brownian surface A Brownian surface is a fractal surface generated via a fractal elevation function. For instance, in the three-dimensional case, where two variables "X" and "Y" are given as coordinates, the elevation function between any two points ("x", "y") and ("x", "y") can be set to have a mean or expected value that increases as the vector distance between ("x", "y") and ("x", "y"). There are, however, many ways of defining the elevation function. For instance, the fractional Brownian motion variable may be used, or various rotation functions may be used to achieve more natural looking surfaces. As with