What is DC level in white gaussian noise?
DC level in signal processing refers to the average or the mean value of a signal. So a zero-mean signal will have an average value of zero over its domain of definition.

When this concept is extended to the stochastic processes, we shall distinguish between time average and ensemble averages. A stochastic process can be viewed as an ensemble of time functions and a sequence of random variables. When a stochastic process is assumed to be ergodic, then its time averages over a sample function equal its ensemble averages over the random variables. In such a case the zero-mean random process creates time functions which have zero averages, hence zero DC levels.