Optimal transport for multifractal random measures. Applications.

Rémi Rhodes (1) , Vincent Vargas (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Random measures; multifractal processes; optimal transport; metric; KPZ

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Rémi Rhodes, Vincent Vargas. Optimal transport for multifractal random measures. Applications.. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011, pp.version électronique. ⟨hal-00512738⟩