Predictability of band-limited, high-frequent, and mixed processes in the presence of ideal low-pass filters

We study pathwise predictability of continuous time processes in deterministic setting, when the convolution integrals over future time can be approximated by integrals over past time. Uniform prediction in some weak sense with respect to certain classes of inputs is discussed. We found that all band-limited processes are predictable in this sense, as well as high-frequent processes with zero energy at low frequencies. It follows that a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.