If it is given that PSD of a random process is bandlimited to frequency $f_B$, then can we claim that any sample path of the random process is also bandlimited to $f_B$?
Intuitively, I always thought of PSD as spectrum of the random signal in some sense but mathematically, the relationship between PSD of the random process and Fourier transform of the random process is not clear to me. If the PSD is limited to $f_B$, then it is a statement on the autocorrelation function of the WSS process. Does this translate to every sample path of the random process being bandlimited to $f_B$ as well?
Edit: For clarity, I'm considering a discrete time random process $X[n]$.