We aim at detecting stress in newborns by observing heart rate variability (HRV). The HRV features nonlinearities. Fractal dynamics is a usual way to model them and the Hurst exponent summarizes the fractal information. In our framework, we have observations of short duration, for which usual estimators of the Hurst exponent, like detrended fluctuation analysis (DFA), are not adapted. Moreover, we observe that the Hurst exponent does not vary much between stress and rest phases, but its decomposition in memory and underlying properties of the probability distribution leads to satisfactory diagnostic tools. This decomposition of the Hurst exponent is in addition embedded in a mean-reverting model. The resulting model is a mean-reverting fractional Lévy stable motion (FLSM). We estimate it and use its parameters as diagnostic tools of neonatal stress. Indeed, the value of the speed of reversion parameter is a significant indicator of stress. The evolution of both parameters in which the Hurst exponent is decomposed provides us with significant indicators as well. On the contrary, the Hurst exponent itself does not bear useful information.

中文翻译：

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基于均值恢复分数 Lévy 稳定运动的新生儿压力中心率变异性的赫斯特指数

我们旨在通过观察心率变异性 (HRV) 来检测新生儿的压力。HRV 具有非线性特征。分形动力学是对其建模的常用方法，Hurst 指数总结了分形信息。在我们的框架中，我们有短期的观察结果，Hurst 指数的常用估计量，如去趋势波动分析 (DFA)，并不适用。此外，我们观察到 Hurst 指数在压力和休息阶段之间变化不大，但它在记忆中的分解和概率分布的基本属性导致了令人满意的诊断工具。赫斯特指数的这种分解另外嵌入到均值回复模型中。生成的模型是均值恢复分数 Lévy 稳定运动 (FLSM)。我们估计它并将其参数用作新生儿压力的诊断工具。事实上，反转速度参数的值是压力的重要指标。赫斯特指数分解的两个参数的演变也为我们提供了重要的指标。相反，Hurst 指数本身并不承载有用的信息。