Optimal transportation for multifractal random measures and applications

Rhodes, Rémi; Vargas, Vincent

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

Number

Publisher

Institute of Mathematical Society

Pages

119-137

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