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Now showing items 1-10 of 12

#### Wavelet Analysis of Fractional Brownian Motion in Multifractal Time

(1999-09-20)

We study <i>fractional Brownian motions in multifractal time</i>, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the ...

#### Conditional and Relative Multifractal Spectra

(1997-03-01)

In the study of the involved geometry of singular distributions the use of fractal and multifractal analysis has shown results of outstanding significance. So far, the investigation has focused on structures produced by one single mechanism which were analyzed with respect to the ordinary metric or volume. Most prominent examples include self-similar ...

#### Exceptions to the Multifractal Formalism for Discontinuous Measures

(1998-01-15)

In an earlier paper the authors introduced the <i>inverse measure</i> <i>Âµ</i><sup>â </sup>(<i>dt</i>) of a given measure <i>Âµ</i>(<i>dt</i>) on [0,1] and presented the 'inversion formula' <i>f</i><sup>â </sup>(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>) which was argued to link the respective multifractal spectra of <i>Âµ</i> and <i>Âµ</i><sup>â ...

#### Numerical Estimates of Generalized Dimensions D_q for Negative q

(1996-01-01)

Usual fixed-size box-counting algorithms are inefficient for computing generalized fractal dimensions D(<i>q</i>) in the range of <i>q</i><0. In this Letter we describe a new numerical algorithm specifically devised to estimate generalized dimensions for large negative <i>q</i>, providing evidence of its better performance. We compute the complete ...

#### Multifractal Formalism for Infinite Multinomial Measures

(1995-01-20)

There are strong reasons to believe that the multifractal spectrum of DLA shows anomalies which have been termed left sided. In order to show that this is compatible with strictly multiplicative structures Mandelbrot et al. introduced a one parameter family of multifractal measures invariant under infinitely many linear maps on the real line. Under ...

#### Inversion Formula for Continuous Multifractals

(1997-01-20)

In a previous paper the authors introduced the inverse measure <i>Âµ</i><sup>â </sup> of a probability measure <i>Âµ</i> on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' <i>f</i><sup>â </sup>(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>). Here, the statements of Part I are put in more mathematical ...

#### Multifractal Properties of TCP Traffic: a Numerical Study

(1997-10-20)

We analyze two traces of TCP--traffic recorded at the gateway of a LAN correÂ sponding to two hours at Berkeley and to eight hours at CNET labs respectively. We are mainly interested in a multifractal approach, which we introduce with varÂ ious examples. We elaborate on the difference to (mono)fractal statistical tests being used so far. Though we ...

#### An Improved Multifractal Formalism and Self Similar Measures

(1995-01-01)

To characterize the geometry of a measure, its so-called generalized dimensions D(<i>q</i>) have been introduced recently. The mathematically precise definition given by Falconer turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative <i>q</i> range. A new ...

#### Inverse Measures, the Inversion formula, and Discontinuous Multifractals

(1997-01-20)

The present paper is part I of a series of three closely related papers in which the inverse measure m' of a given measure m on [0,1] is introduced. In the first case discussed in detail, both these measures are multifractal in the usual sense, that is, both are linearly self-similar and continuous but not differentiable and both are non-zero for ...

#### A Simple Statistical Analysis of Wavelet-based Multifractal Spectrum Estimation

(1998-11-01)

The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. In this paper, we derive asymptotic expressions for the bias and variance of a wavelet-based ...