A turning-band method for the simulation of anisotropic fractional Brownian fields [Working Paper]

Abstract : In this paper, we propose a method for simulating realizations of two-dimensional anisotropic fractional Brownian fields (AFBF) introduced by Bonami and Estrade (2003). The method is adapted from a generic simulation method called the turning-band method (TBM) due to Matheron (1973). The TBM reduces the problem of simulating a field in two dimensions by combining independent processes simulated on oriented bands. In the AFBF context, the simulation fields are constructed by solving an integral equation arising from the application of the TBM to non-stationary anisotropic fields. This garantees the convergence of simulations as their precision is increased. The construction is followed by a theoretical study of the convergence rate. Another key feature of this work is the simulation of band processes. Using self-similarity properties, processes are simulated exactly on bands with a circulant embedding method, so that simulation errors are exclusively due to the field approximation. Moreover, we design a Dynamic Programming algorithm that selects band orientations achieving the optimal trade-off between computational cost and precision. Finally, we conduct a numerical study showing that the approximation error does not significantly depend on the regularity of the fields to be simulated, nor on their degree of anisotropy. Experiments also suggest that simulations preserve field statistical properties.
Type de document :
Pré-publication, Document de travail
MAP5 2012-31. 2012
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00741167
Contributeur : Lionel Moisan <>
Soumis le : jeudi 11 octobre 2012 - 21:53:59
Dernière modification le : mercredi 16 novembre 2016 - 11:30:51
Document(s) archivé(s) le : samedi 17 décembre 2016 - 00:18:08

Fichier

2012-31.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00741167, version 1

Collections

Citation

Hermine Biermé, Lionel Moisan, Frédéric Richard. A turning-band method for the simulation of anisotropic fractional Brownian fields [Working Paper]. MAP5 2012-31. 2012. <hal-00741167>

Partager

Métriques

Consultations de
la notice

659

Téléchargements du document

450