A Geometric Brownian Motion is a Brownian Motion with a drift.

It is determined by:

\begin{equation} \dd{S_{t}} = \mu S_{t} \dd{t} + \sigma \dd{S_{t}} \dd{W_{t}} \end{equation}

where, \(S_{t}\) is a Geometric Brownian Motion, \(\mu\) is its drift, \(\sigma\) the volatility, and \(W_{t}\) a centered Brownian Motion.