Optimal transportation for multifractal random measures and applications

Rémi Rhodes; Vincent Vargas

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 1, page 119-137
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Rhodes, Rémi, and Vargas, Vincent. "Optimal transportation for multifractal random measures and applications." Annales de l'I.H.P. Probabilités et statistiques 49.1 (2013): 119-137. <http://eudml.org/doc/271953>.

@article{Rhodes2013,
abstract = {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.},
author = {Rhodes, Rémi, Vargas, Vincent},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random measures; multifractal processes; optimal transportation; random metric},
language = {eng},
number = {1},
pages = {119-137},
publisher = {Gauthier-Villars},
title = {Optimal transportation for multifractal random measures and applications},
url = {http://eudml.org/doc/271953},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Rhodes, Rémi
AU - Vargas, Vincent
TI - Optimal transportation for multifractal random measures and applications
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 1
SP - 119
EP - 137
AB - 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.
LA - eng
KW - random measures; multifractal processes; optimal transportation; random metric
UR - http://eudml.org/doc/271953
ER -

References

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  1. [1] E. Bacry and J. F. Muzy. Log-infinitely divisible multifractal processes. Comm. Math. Phys.236 (2003) 449–475. Zbl1032.60046MR2021198
  2. [2] I. Benjamini and O. Schramm. KPZ in one dimensional random geometry of multiplicative cascades. Comm. Math. Phys.289 (2009) 653–662. Zbl1170.83006MR2506765
  3. [3] B. Duplantier and S. Sheffield. Liouville quantum gravity and KPZ. Invent. Math.185 (2011) 333–393. Zbl1226.81241MR2819163
  4. [4] A. H. Fan. Sur le chaos de Lévy d’indice 0 l t ; α l t ; 1 . Ann. Sci. Math. Québec21 (1997) 53–66. Zbl0884.60040
  5. [5] J.-P. Kahane. Sur le chaos multiplicatif. Ann. Sci. Math. Québec9 (1985) 105–150. Zbl0596.60041MR829798
  6. [6] R. Rhodes and V. Vargas. KPZ formula for log-infinitely divisible multifractal random measures. ESAIM Probab. Stat.15 (2011) 358–371. Zbl1268.60070MR2870520
  7. [7] R. Rhodes and V. Vargas. Multidimensional multifractal random measures. Electron. J. Probab.15 (2010) 241–258. Zbl1201.60046MR2609587
  8. [8] C. Villani. Optimal Transport, Old and New. Grundlehren Math. Wiss. 338. Springer, Berlin. Zbl1156.53003MR2459454
  9. [9] C. Villani. Topics in Optimal Transportations. Grad. Stud. Math. 58. Amer. Math. Soc., Providence, RI, 2003. Zbl1106.90001MR1964483
  10. [10] E. C. Waymire and S. C. William. Multiplicative cascades: Dimension spectra and dependence. J. Fourier Anal. Appl. (Special Issue: Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay, 1993)) (1995) 589–609. Zbl0889.60050MR1364911

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