If you'll look up for the definition of a (discrete) white noise process on the web, you'll find some sources that say:
"white noise is defined by zero mean, finite and constant variance, zero autocorrelation"
and roughly the same amount of them that say:
"white noise is defined by zero mean, finite variance, zero autocorrelation".
In the latter (e.g. the Wikipedia page), "white noise" encompasses also the case of heteroskedastic white noise - where the variance isn't constant. Obviously, stationarity is dropped.
Which of these two is "the" standard definition? Am I missing something?