A Survey on Prescription of Multifractal Behavior
Résumé
Multifractal behavior has been identified and mathematically established for large classes of functions, stochastic processes and measures. Multifractality has also been observed on many data coming from Geophysics, turbulence, Physics, Biology, to name a few. It is thus natural to develop mathematical models whose scaling and multifractal properties fit those measured on data. This raises several still unsolved theoretical questions about the prescription of multifractality (i.e. how to build mathematical models with a multifractal spectrum known in advance), typical behavior in function spaces, and existence of solutions of PDEs or SPDEs with possible multifractal behavior. In this survey, we list some of the latest results in this area.
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