why power spectral density rather than DFT for non-deterministic or random signals

As we see for the existence of continuous or discrete Fourier transform the Dirichlet conditions which are three in number.

1) first it should be a finite energy signal
2) the signal should have finite number of discontinuities
3) It should have finite number of maxima and minima

But non deterministic signal viloate atleast one of these, so fourier transform does not exist for these random signals.


But the power spectral density is defined,valid and it exists.
it does not have phase information but this is the only way the signal can be represnted in frequency domain.