Editing Geometric Brownian motion (section)

==Technical definition: the SDE==

A stochastic process ''S''<sub>''t''</sub> is said to follow a GBM if it satisfies the following [[stochastic differential equation]] (SDE):

:<math> dS_t = \mu S_t\,dt + \sigma S_t\,dW_t </math>

where <math> W_t </math> is a [[Wiener process|Wiener process or Brownian motion]], and <math> \mu </math> ('the percentage drift') and <math> \sigma </math> ('the percentage volatility') are constants.

The former parameter is used to model deterministic trends, while the latter parameter models unpredictable events occurring during the motion.