In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coeecients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing N-point data sets. We study both the s...

Title of Dissertation: MULTIFRACTAL INTERNET TRAFFIC MODEL AND ACTIVE QUEUE MANAGEMENT Jia-Shiang Jou, Doctor of Philosophy, 2003 Dissertation directed by: Professor John S. Baras Department of Electrical and Computer Engineering We propose a multilevel (hierarchical) ON/OFF model to simultaneously capture the mono/multifractal behavior of Internet traffic. Parameter estimation methods are deve...

Previous works related to the application of multifractal theory for analyzing grain size distribution (GSD), showed potential this approach deal with complex issue. However, absence practical kind statistical analysis raised some doubts among soil scientists. Compared experimental dry sieving method, which is based on mass representations different sizes, presented in work relies densities (de...

We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with tailed distribution of off-diagonal elements form large-deviation ansatz. present general theory survival probability such random-matrix model show that {\it averaged} may decay time as simple exponent, stretch-exponent power-law or slower. Correspondingly, we identify exponential, stretch-exponent...

We propose and illustrate a Markov-switching multi-fractal duration (MSMD) model for analysis of inter-trade durations in financial markets. We establish several of its key properties with emphasis on high persistence (indeed long memory). Empirical exploration suggests MSMD’s superiority relative to leading competitors. Acknowledgments: For outstanding research assistance we thank Matthew Klei...

This paper generalizes Poisson-Multifractal for correlated time series of count data. We show that the model has useful properties; it captures long-term time dependence and exible dependence between types of count. Based on real data, the correlated multifractal model is used to model the number of claims of two separate coverages in automobile insurance. Smoothed values of the underlying proc...

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, ...

Possibilities of utilizing multifractal analysis in teletraffic modeling and characterization are examined. Three standard traffic models are studied by using multifractal approach. Furthermore, multifractal properties of real ATM traffic recorded at Technical University of Tampere are considered.

Multifractal theory provides a new spatial analytical tool to describe urban form and growth, but many basic problems remain to be solved. Among various pending issues, the most significant one is how to obtain proper multifractal dimension spectrums. If an algorithm is improperly used, the parameter values will be abnormal. This paper is devoted to drawing a comparison between two OLS-based ap...