Fractional Poisson field and Fractional Brownian field: why are they resembling but different? - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Electronic Communications in Probability Année : 2013

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

Résumé

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.
Fichier principal
Vignette du fichier
ShortPoisson.pdf (250.16 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00686573 , version 1 (10-04-2012)

Identifiants

  • HAL Id : hal-00686573 , version 1

Citer

Hermine Biermé, Yann Demichel, Anne Estrade. Fractional Poisson field and Fractional Brownian field: why are they resembling but different?. Electronic Communications in Probability, 2013, 18, pp.1--13. ⟨hal-00686573⟩
248 Consultations
205 Téléchargements

Partager

Gmail Facebook X LinkedIn More