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Optimal transportation for multifractal random measures and applications

Rhodes, Rémi; Vargas, Vincent (2013), Optimal transportation for multifractal random measures and applications, Annales de l'I.H.P. Probabilités et Statistiques, 49, 1, p. 119-137. http://dx.doi.org/10.1214/11-AIHP443

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http://hal.archives-ouvertes.fr/hal-00512738/fr/
Date
2013
Nom de la revue
Annales de l'I.H.P. Probabilités et Statistiques
Volume
49
Numéro
1
Éditeur
Institute of Mathematical Society
Pages
119-137
Identifiant publication
Métadonnées
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Auteur(s)
Rhodes, Rémi
Vargas, Vincent
Résumé (EN)
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures. This study is motivated by recent problems in the KPZ context.
Mots-clés
KPZ; Random measures; multifractal processes; optimal transport; metric