Optimal transportation for multifractal random measures and applications
Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 1, p. 119-137

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.

Dans ce papier, nous étudions des problèmes de transport optimal pour des mesures aléatoires multifractales. Puisque ces mesures sont beaucoup moins régulières que ce que la théorie requiert habituellement, nous introduisons une nouvelle notion de transport qui peut être vue intuitivement comme du transport à étapes multiples. En application, nous construisons des changements de temps multifractals et nous établissons l'existence de métriques aléatoires pour lesquelles les formes volume sont des mesures aléatoires multifractales.

DOI : https://doi.org/10.1214/11-AIHP443
Classification:  60G57,  49J55,  28A80,  28A75
Keywords: random measures, multifractal processes, optimal transportation, random metric
@article{AIHPB_2013__49_1_119_0,
     author = {Rhodes, R\'emi and Vargas, Vincent},
     title = {Optimal transportation for multifractal random measures and applications},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {1},
     year = {2013},
     pages = {119-137},
     doi = {10.1214/11-AIHP443},
     mrnumber = {3060150},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_1_119_0}
}
Rhodes, Rémi; Vargas, Vincent. Optimal transportation for multifractal random measures and applications. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 1, pp. 119-137. doi : 10.1214/11-AIHP443. http://www.numdam.org/item/AIHPB_2013__49_1_119_0/

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