Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes

TL;DR

This paper investigates the power-law scaling behavior in a non-Markovian, nonlinear point process driven by fractional Brownian motion, and demonstrates that a nonlinear Markovian process can replicate this scaling, suggesting a link between nonlinearity and non-Markovian features.

Contribution

It reveals that nonlinear Markovian processes can mimic the power-law scaling of non-Markovian processes driven by fractional Brownian motion.

Findings

Power-law scaling observed in the process's event count and spectral density.

Nonlinear Markovian processes can reproduce non-Markovian scaling behavior.

Abstract

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non--Markovian point process exhibit power--law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a possible link between nonlinearity and apparent non--Markovian behavior.