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.

中文翻译：

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非马尔可夫和非线性点过程的幂律缩放行为的相似性

我们分析了由受限分数布朗运动驱动的时间点过程的统计特性。这种非马尔可夫点过程的事件计数分布和功率谱密度表现出幂律缩放。我们表明非线性马尔可夫点过程可以重现相同的缩放行为。该结果表明非线性和明显的非马尔可夫行为之间可能存在联系。