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Optimal transportation for multifractal random measures and applications

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GeodKPZ.pdf (324.5Kb)
Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00512738/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
KPZ; Random measures; multifractal processes; optimal transport; metric
Journal issue
Annales de l'I.H.P. Probabilités et Statistiques
Volume
49
Number
1
Publication date
2013
Article pages
119-137
Publisher
Institute of Mathematical Society
DOI
http://dx.doi.org/10.1214/11-AIHP443
URI
https://basepub.dauphine.fr/handle/123456789/4695
Collections
  • CEREMADE : Publications
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Author
Rhodes, Rémi
Vargas, Vincent
Type
Article accepté pour publication ou publié
Abstract (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.

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