On detecting and quantification of randomness for one-sided sequences

Abstract

The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based on frequency analysis of two-sided and one-sided sequences. In addition, the paper suggests an extension of the notion of bandlimitiness on one-sided sequences and a procedure allowing to represent an one-sided sequence as a sum of left-bandlimited and predictable sequences and a non-reducible noise.