Multidimensional multifractal random measures.
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [ (2009)] and improves this latter work by considering possibly degenerate...
On homogenization of space-time dependent and degenerate random flows II
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. 236 (2003) 449–475]. If is a non degenerate multifractal measure with associated metric () = ([]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dim of a measurable set and the Hausdorff dimension dim with respect to of the same set: ζ(dim ()) = dim(). Our results can be...
Optimal transportation for multifractal random measures and applications
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.
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. (2003) 449–475]. If is a non degenerate multifractal measure with associated metric () = ([]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dim of a measurable set and the Hausdorff dimension dim with respect to of the same set: ζ(dim ()) = dim(). Our results...
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