Pathwise continuous time spectrum degeneracy at a single point and weak predictability

The paper studies properties of continuous time processes in pathwise deterministic setting with spectrum degeneracy at a single point where their Fourier transforms vanish. It appears that these processes are predictable is some weak sense, meaning that convolution integrals over future time can be approximated by integrals over past time. In particular, this means that the processes with this degeneracy are uniquely defined by their past values on the semi-infinite intervals. Corresponding predictors are obtained. The predictors feature some robustness with respect to noise contamination.