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The Hurst Exponent of Heart Rate Variability in Neonatal Stress, Based on a Mean-Reverting Fractional Lévy Stable Motion

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.