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- Antoine Echelard
- 2012

We propose a new model for RR interval records based on the empirical finding that the amplitude of RR records is negatively correlated with its regularity. We develop the mathematics needed to define rigorously this model, as well as the statistical tools necessary for estimating the parameters of the model on sampled data. We use this to analyze finely… (More)

Approximate scale-invariance and local regularity properties of natural terrains suggest that they can be a accurately modeled with random processes which are locally fractal. Current models for terrain modeling include fractional and multifractional Brownian motion. Though these processes have proved useful, they miss an important feature of real terrains:… (More)

We present a denoising method that is well fitted to the processing of extremely irregular signals such as (multi)fractal ones. Such signals are often encountered in practice, e.g., in biomedical applications. The basic idea is to estimate the regularity of the original data from the observed noisy ones using the large scale information, and then to… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract We construct functions and stochastic processes for which a functional relation holds between amplitude and local regularity, as measured by the pointwise or local Hölder exponent. We consider in particular functions and processes built by extending Weierstrass function, multifractional Brownian… (More)

The large deviation multifractal spectrum is a function of central importance in multifractal analysis. It allows a ne description of the distribution of the singularities of a function over a given domain. The 2-microlocal spectrum, on the other hand, provides an extremely precise picture of the regularity of a distribution at a point. These two spectra… (More)

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