On detecting and quantification of randomness for one-sided sequences

TL;DR

This paper explores methods to detect and quantify randomness in deterministic one-sided sequences, extending bandlimit concepts and decomposing sequences into predictable and noise components without probabilistic assumptions.

Contribution

It introduces new approaches for randomness quantification and extends the bandlimit concept to one-sided sequences, enabling sequence decomposition into predictable parts and noise.

Findings

Proposes frequency-based measures for randomness quantification.

Extends bandlimit notions to one-sided sequences.

Provides a decomposition method into predictable and noise components.

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.