Wiener process | Non-Newtonian calculus

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. (Wikipedia).

Geometric Brownian motion
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Related pages

Wiener process | Black–Scholes model | Quadratic variation | Stochastic differential equation | Probability density function | Stochastic drift | Logarithm | Stochastic process | Itô's lemma | Heat kernel | Brownian motion | Martingale (probability theory) | Itô calculus | Stochastic volatility | Log-normal distribution | Variance | Dirac delta function | Heat equation | Brownian surface | Mathematical finance | Random variable | Expected value