|WikiProject Statistics||(Rated Start-class, Low-importance)|
"The drift rate of zero means that the expected value of an stochastic variable at any future time is equal to the current value. The standard Brownian motion process has a drift rate of zero and a variance of one." http://investment-and-finance.net/derivatives/d/drift-rate.html
The above statement should be exemplified for clarity as proposed in the edits of the first paragraph.
Problem: the Wiki Article states: "A related term is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of coin tosses has a drift rate of 1/2 per toss. "
The average of a sum of coin tosses does not change 1/2 per toss. The average changes on order 1/2n per toss. Thus the example does not illustrate the drift rate well. The sum changes 0 or 1 per toss, assuming 1=heads and 0=tails. So the sum is expected to change an average of 1/2 per toss. The sum is not the average.
Proposing the following wording:
"The drift rate of a coin toss process is zero and the variance is 1/2, assuming 1=heads and 0=tails."