Fractional Poisson field and Fractional Brownian field: why are they resembling but different?

Abstract : The fractional Poisson field (fPf) is constructed by considering the number of balls falling down on each point of R^D, when the centers and the radii of the balls are thrown at random following a Poisson point process in R^D\times R^+ with an appropriate intensity measure. It provides a simple description for a non Gaussian random field that is centered, has stationary increments and has the same covariance function as the fractional Brownian field (fBf). The present paper is concerned with specific properties of the fPf, comparing them to their analogues for the fBf. On the one hand, we concentrate on the finite-dimensional distributions which reveal strong differences between the Gaussian world of the fBf and the Poissonnian world of the fPf. We provide two different representations for the marginal distributions of the fPf: as a Chentsov field, and on a regular grid in R^D with a numerical procedure for simulations. On the other hand, we prove that the Hurst index estimator based on quadratic variations which is commonly used for the fBf is still strongly consistent for the fPf. However the computations for the proof are very different from the usual ones.
Type de document :
Article dans une revue
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.1--13
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00686573
Contributeur : Hermine Biermé <>
Soumis le : mardi 10 avril 2012 - 15:55:35
Dernière modification le : mardi 10 octobre 2017 - 11:22:04
Document(s) archivé(s) le : mercredi 11 juillet 2012 - 02:54:13

Fichier

ShortPoisson.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00686573, version 1

Collections

Citation

Hermine Biermé, Yann Demichel, Anne Estrade. Fractional Poisson field and Fractional Brownian field: why are they resembling but different?. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.1--13. 〈hal-00686573〉

Partager

Métriques

Consultations de la notice

285

Téléchargements de fichiers

157