Power spectral density vs Energy spectral density
Random process is never ending, non-periodic phenomenon, so taking Fourier transform of its realizations makes no sense, not possible either. However if random process is stationary, then it is for sure that it has some finite power over some band of frequencies. Now, here the question arises that how to compute the power of this stationary random process, (fourier tranform is not possible to be taken directly)? So, what to do? we find the auto-correlation function of the given random process, whose fourier transform always exist. Finally, we take the fourier tranform of this autocorrelation function to get the power spectral density of the given stationary process.

If you integrate the power spectral density of a given stationary process over the interval from -$\infty$ to $\infty$ you ll get the total power contained in the given random process.