Editing Geometric Brownian motion (section)

{{Short description|Continuous stochastic process}}
[[File:GBM2.png|thumb|400x400px|For the simulation generating the realizations, see below.]]
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 [[stochastic drift|drift]].<ref>{{cite book |title=Introduction to Probability Models |first=Sheldon M. |last=Ross |location=Amsterdam |publisher=Elsevier |edition=11th |year=2014 |chapter=Variations on Brownian Motion |pages=612–14 |isbn=978-0-12-407948-9 |chapter-url=https://books.google.com/books?id=A3YpAgAAQBAJ&pg=PA612 }}</ref> 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]].