KPZ formula for log-infinitely divisible multifractal random measures
Rhodes, Rémi; Vargas, Vincent (2011), KPZ formula for log-infinitely divisible multifractal random measures, ESAIM. Probability and Statistics, 15, p. 358-371. http://dx.doi.org/10.1051/ps/2010007
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00293878/en/
Journal nameESAIM. Probability and Statistics
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Abstract (EN)We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in . If M is a non degenerate multifractal measure with associated metric ρ(x, y) = M ([x, y]) and structure function ζ , we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a mea- surable set K and the Hausdorff dimension dimρ H with respect to ρ of the same set: ζ (dimρ (K)) = dimH (K). Our results can be extended to higher dimensions in the log normal case: inspired by quantum gravity in dimension 2, we consider the 2 dimensional case.
Subjects / KeywordsMultifractal processes.; Random measures; Hausdorff dimensions
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