论文标题
关于多重行为处方处方的调查
A survey on prescription of multifractal behavior
论文作者
论文摘要
已经确定并在数学上确定了多类行为，并为大量的功能，随机过程和度量确定。在许多来自地球物理，湍流，物理，生物学的数据中也观察到了多种纹理，仅举几例。因此，开发其比例和多重分裂特性符合数据的数学模型是一个重要的问题。这就提出了几个关于多种纹理处方的仍未解决的理论问题（即如何以奇异性频谱构建数学模型），功能空间中的典型行为以及具有可能的多帧性行为的PDE或SPDE的解决方案。在这项调查中，我们收集了该领域的一些最新结果。专门针对开发数据分析小波工具的先驱Alain Arn {é} Odo。
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. Developing mathematical models whose scaling and multifractal properties fit those measured on data is thus an important issue. This raises several still unsolved theoretical questions about the prescription of multifractality (i.e. how to build mathematical models with a singularity spectrum known in advance), typical behavior in function spaces, and existence of solutions to PDEs or SPDEs with possible multifractal behavior. In this survey, we gather some of the latest results in this area. Dedicated to Alain Arn{é}odo, pioneer in the development of wavelet tools for data analysis.
