Multifractal analysis of sums of random pulses

用连续小波变换刻画 p-指数及其在随机脉冲和的多重分形分析中的应用

Characterization of p-exponents by continuous wavelet transforms, applications to the multifractal analysis of sum of random pulses

本文提出用连续小波变换刻画 p-指数的新方法，并将其应用于随机脉冲和的正则性分析，从而为齐次自相似过程的多重分形谱估计提供更易用的工具。

Multifractal tubes

Tube formulas refer to the study of volumes of $r$ neighbourhoods of sets. For sets satisfying some (possible very weak) convexity conditions, this has a long history. However, within the past 20 years Lapidus has initiated and pioneered a systematic study of tube formulas for fractal sets. Following this, it is natural to ask to what extend it is possible to develop a theory of multifractal tube formulas for multifractal measures. In this paper we propose and develop a framework for such a theory. Firstly, we define multifractal tube formulas and, more generally, multifractal tube measures fo…