Section: New Results

Large deviations estimates for the multiscale analysis of heart rate variability

In the realm of multiscale signal analysis, multifractal analysis provides with a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multi- fractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory al- lows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large devia- tions singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large devia- tions principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiolog- ical characteristics. In particular we quantify the presence/absence of scale invariance of RR signals.

These results gather most achievements we carried out within the ANR project DMASC.