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

摘要

Pathwise predictability of continuous time processes is studied indeterministic setting. We discuss uniform prediction in some weak sense withrespect to certain classes of inputs. More precisely, we study possibility ofapproximation of convolution integrals over future time by integrals over pasttime. We found that all band-limited processes are predictable in this sense,as well as high-frequency processes with zero energy at low frequencies. Itfollows that a process of mixed type still can be predicted if an ideallow-pass filter exists for this process.