Wolfram Alpha:

```Brownian Motion
---------------

Brownian motion (named after the Scottish botanist Robert Brown)
is the seemingly random movement of particles suspended in a fluid
(i.e. a liquid such as water or air) or the mathematical model used
to describe such random movements, often called a particle theory.
The following animated gif demonstrates such a motion.  The big
particle can be considered as a dust particle while the smaller
particles can be considered as the molecules of a gas.

ln(St/St-1) = αΔt + Wtσ

It has been shown that the logarithms of common stock prices
have aprobability distribution that is very similar to the
probability distribution for a particle in Brownian motion.
The model for stock price evolution is given by:

ln(St/St-1) = αΔt + Wtσ

Where,
ln is the natural logarithm.
St is the stock price in the current period.
St-1 is the stock in the previous period.
α = μ - 0.5σ2 is the "adjusted drift" for the stock.
Δt is the change in time.
μ is the drift of the stock.
σ is the volatility of the stock.
Wt = ε√t ... the Brownian motion.
ε is a random number drawn from the Inverse Standard Normal
cumulative distribution, N(0,1).

The first term is the "drift" component and the second term is
the "shock or uncertainty" component. ```