Field measurements of conductivity, porosity, etc. have shown their are high heterogeneity, the bounds of such heterogeneity increasing as the scale of observations changes. This has led to the development of fractal models, renormgroup methods, and methods of subgrid modeling. The subgrid modeling approach, associated with problems of the subsurface hydrodynamics, is presented. We consider a s...

In this paper we develop a new multiscale modeling framework for characterizing positive valued data with long range dependent correlations f noise Using the Haar wavelet transform and a special multi plicative structure on the wavelet and scaling coe cients to ensure positive results the model provides a rapid O N cascade algorithm for synthesizing N point data sets We study both the second or...

In this thesis, we consider two classes of stochastic models which both capture some of the essential properties of teletraffic. Teletraffic has two time regimes where profoundly different behavior and characteristics are seen. When traffic traces are observed at coarse resolutions, properties like self-similarity and longrange dependence are visible. In small time-scales, traffic exhibits comp...

The multifractal framework relates the scaling properties of turbulence to its local regularity properties through a statistical description as a collection of local singularities. The multifractal properties are moreover linked to the multiplicative cascade process that creates the peculiar properties of turbulence such as intermittency. A comprehensive estimation of the multifractal propertie...

In various fields, such as teletraffic and economics, measured times series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a non-stationary process. To overcome this problem we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a...

Analysis of the cardiovascular system (CVS) activity is important for several purposes, including better understanding of heart physiology, diagnosis and forecast of cardiac events. The central CVS, through the study of heart rate variability (HRV), has been shown to exhibit multifractal properties, possibly evolving with physiologic or pathologic states of the organism. An additional viewpoint...

This is an easy read introduction to multifractals We start with a thorough study of the Binomial measure from a multifractal point of view introducing the main multifractal tools We then continue by showing how to generate more general multiplicative measures and close by presenting an extensive set of examples on which we elaborate how to read a multifractal spectrum

Abstract. We present the results on the modelling and synthesis of broadband traffic processes namely ethernet inter-arrival times using the VVGM (variable variance gaussian multiplier) multiplicative multifractal model. This model is shown to be more appropriate for modelling network traffic which possess time varying scaling/self-similarity and burstiness. The model gives a simple and efficie...

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localizat...

Multifractal fluctuations in the time dynamics of geoelectrical data, recorded in a seismic area of southern Italy, have been revealed using the Multifractal Detrended Fluctuation Analysis (MF-DFA), which allows to detect multifractality in nonstationary signals. Our findings show that the geoelectrical time series, recorded in the seismic area of southern Apennine Chain (Italy), is multifracta...