Generalization of Campbell's theorem to nonstationary noise

Campbell's theorem is a fundamental result in noise theory and is applied in many fields of science and engineering. It gives a simple but very powerful expression for the mean and standard deviation of a stationary random pulse train. We generalize Campbell's theorem to the non-stationary case where the random process is space and time dependent. We also generalize it to a pulse train of waves, acoustic and electromagnetic, where the intensity is defined as the absolute square of the pulse train.