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Statistical estimation of a class of self-regulating processes

Abstract : Self-regulating processes are stochastic processes whose local regularity, as measured by the pointwise Hölder exponent, is a function of amplitude. They seem to provide relevant miodels for various signals arising e.g. in geophysics and biomedicine. We propose in this work an estimator of the self-regulating function (that is, the function relating amplitude and Hölder regularity) of the self-regulating midpoint displacement process introduced in [4] and study some of its properties. We prove that it is almost surely convergent and obtain a central limit theorem. Numerical simulations show that the estimator behaves well in practice.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-00868604
Contributor : Lisandro Fermin <>
Submitted on : Tuesday, October 1, 2013 - 4:19:23 PM
Last modification on : Thursday, April 5, 2018 - 10:36:48 AM
Long-term archiving on: : Thursday, January 2, 2014 - 9:00:13 AM

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  • HAL Id : hal-00868604, version 1

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Antoine Echelard, Jacques Lévy Véhel, Anne Philippe. Statistical estimation of a class of self-regulating processes. 2013. ⟨hal-00868604v1⟩

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