Power contained in a random process $X(t)$
Assuming that the process is wide-sense-stationary, the total power in a random process with autocorrelation function $R(\tau)$ and power spectral density $S(f) = \mathcal F\{R(\tau)\}$ is given by
$$\text{Total Power} = \int_{-\infty}^\infty S(f) \,\mathrm df = R(0)$$ while the "DC power" (also equal to the squared mean of the process)  is given by
$$\text{DC Power} = \lim_{\tau \to \infty} R(\tau).$$ The DC power is also given by the magnitude or amplitude of the impulse (if any) at the origin in $S(f)$. Note that $S(0)&gt; 0$ is not enough to claim that the  process has DC power -- for example, white noise has no DC power --; we need to have an impulse (a.k.a Dirac delta) at the origin in $S(f)$ for the process to have DC power.

What the AC power might be is left as an exercise for the reader to figure out.