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A stochastic process $S$ is defined as following geometric Brownian motion if it satisfies the stochastic differential equation $dS = \mu S\,dt + \sigma S\,dW$, where $\mu$ and $\sigma$ are constants representing the drift and volatility, and $W$ is a standard Brownian motion.

Conditions: $\mu$ and $\sigma$ are constants.; $W$ is a standard Brownian motion.

A stochastic process $S$ is defined as following geometric Brownian motion if it satisfies the stochastic differential equation $dS = \mu S\,dt + \sigma S\,dW$, where $\mu$ and $\sigma$ are constants representing the drift and volatility, and $W$ is a standard Brownian motion.

Conditions: $\mu$ and $\sigma$ are constants.; $W$ is a standard Brownian motion.