1/f noise from point process and time-subordinated Langevin equations

TL;DR

This paper explores how the distinction between internal and physical time in stochastic models can generate 1/f noise, providing a generalized framework that explains its occurrence across various systems.

Contribution

It introduces a generalized stochastic differential equation model linking internal and physical time, demonstrating how this relationship produces 1/f noise over a broad frequency range.

Findings

1/f noise emerges from the relation between internal and physical time.

The model generalizes previous point process approaches.

Applicable to explaining 1/f noise in diverse systems.

Abstract

Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise. After demonstrating the appearance of 1/f noise in the earlier proposed point process model, we generalize it starting from a stochastic differential equation which describes a Brownian-like motion in the internal (operational) time. We consider this equation together with an additional equation relating the internal time to the external (physical) time. We show that the relation between the internal time and the physical time that depends on the intensity of the signal can lead to 1/f noise in a wide interval of frequencies. The present model can be useful for the explanation of the appearance of 1/f noise in different systems.