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.