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Reference.org
Geometric Brownian motion
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<p>A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time <a href="/facts/Stochastic_process/Ng1n1dnB">stochastic process</a> in which the <a href="/facts/Logarithm/QeXaV97q">logarithm</a> of the randomly varying quantity follows a <a href="/facts/Brownian_motion/Th0g0wkr">Brownian motion</a> (also called a <a href="/facts/Wiener_process/KPh7vYd7">Wiener process</a>) with <a href="/facts/Stochastic_drift/GLvKoSbt">drift</a>. It is an important example of stochastic processes satisfying a <a href="/facts/Stochastic_differential_equation/ol9a9WNq">stochastic differential equation</a> (SDE); in particular, it is used in <a href="/facts/Mathematical_finance/P9otEltQ">mathematical finance</a> to model stock prices in the <a href="/facts/Black%25E2%2580%2593Scholes_model/TPPG5YWQ">Black–Scholes model</a>. </p>