A type of Markov process; a stochastic process, i.e., a group of random variables defined on the same probability space which satisfies a set of conditions. In this process, the change in a variable during each short period of time follows a normal distribution (a variable with arithmetic Brownian motion) with a mean equal to zero and a variance equal to that short transition in time. However, a variable whose is defined by geometric Brownian motion has a lognormal probability distribution and will always have a positive mean.

Brownian motion is a founding block for many security price models as well as for option pricing.

It is also known as Wiener process (also, Wiener/ Bachelier process).