Formally, et is a white noise process if E(et) = 0, E(et2) = s2, and E(etej) = 0 for t not equal to j, where all those expectations are taken prior to times t and j.
A common, slightly stronger condition is that they are independent from one another; this is an "independent white noise process."
Often one assumes a normal distribution for the variables, in which case the distribution was completely specified by the mean and variance; these are "normally distributed" or "Gaussian" white noise processes.
Terms related to White Noise Process:
About.Com Resources on White Noise Process:
Writing a Term Paper? Here are a few starting points for research on White Noise Process:
Books on White Noise Process:
Journal Articles on White Noise Process: