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

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.

10 pages, 4 figures

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Cited by in corpus (2)

• Anomalous diffusion and long-range memory in the scaled voter model
• Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions