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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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Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00512738/fr/
Date
2013
Journal name
Annales de l'I.H.P. Probabilités et Statistiques
Volume
49
Number
1
Publisher
Institute of Mathematical Society
Pages
119-137
Publication identifier
http://dx.doi.org/10.1214/11-AIHP443
Metadata
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Author(s)
Rhodes, Rémi
Vargas, Vincent
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.
Subjects / Keywords
KPZ; Random measures; multifractal processes; optimal transport; metric

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