If the change in a small period of time is independent, with a standardized normal distribution (0,1), then z follows the basic Wiener process (Brownian motion). ; for any period T, z = normal(0,T)
A generalized Wiener process of variable x: , where a and b are constants
In a , the change
has a normal distribution with an expected drift rate of a and a variance of .
x in any time interval T is normally distributed with mean of change in x = aT, and variance of change in x =