scholarly journals Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles

2008 ◽  
Vol 36 (3) ◽  
pp. 1404-1434 ◽  
Author(s):  
Jean-François Coeurjolly
Keyword(s):  
Gaussian Processes ◽  
Hurst Exponent ◽  
Self Similar ◽  
Sample Quantiles

scholarly journals Symmetric Stochastic Integrals with Respect to a Class of Self-similar Gaussian Processes

2018 ◽  
Vol 32 (3) ◽  
pp. 1105-1144
Author(s):  
Daniel Harnett ◽  
Arturo Jaramillo ◽  
David Nualart
Keyword(s):  
Gaussian Processes ◽  
Stochastic Integrals ◽  
Self Similar

scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (renewed version-2)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
One Dimensional ◽  
Temporal Series ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals WAVELET-BASED MULTIFRACTAL FORMALISM TO ASSIST IN DIAGNOSIS IN DIGITIZED MAMMOGRAMS

2011 ◽  
Vol 20 (3) ◽  
pp. 169 ◽  
Author(s):  
Pierre Kestener ◽  
Jean Marc Lina ◽  
Philippe Saint-Jean ◽  
Alain Arneodo
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Computer Assisted ◽  
Scaling Properties ◽  
Multifractal Formalism ◽  
Long Range Correlations ◽  
Multifractal Scaling ◽  
Self Similar ◽  
Assisted Diagnosis

We apply the 2D wavelet transform (WTMM) method to perform a multifractal analysis of digitized mammograms. We show that normal regions display monofractal scaling properties as characterized by the socalled Hurst exponent H =0.3±0.1 in fatty areas which look like antipersistent self-similar random surfaces, while H=0.65±0.1 in dense areas which exibit long-range correlations and possibly multifractal scaling properties. We further demonstrate that the 2D WTMM method provides a very efficient way to detect tumors as well as microcalcifications (MC) which correspond to much stronger singularities than those involved in the background tissue roughness fluctuations. These preliminary results indicate that the texture discriminatory power of the 2D WTMM method may lead to significant improvement in computer-assisted diagnosis in digitized mammograms.

scholarly journals Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 196 ◽  
Author(s):  
Orietta Nicolis ◽  
Jorge Mateu ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Shannon Entropy ◽  
Simulation Study ◽  
Hurst Exponent ◽  
Wavelet Spectrum ◽  
Two Dimensional ◽  
Entropy Measures ◽  
Rényi Entropies ◽  
Self Similar ◽  
Fractional Brownian Field ◽  
Renyi Entropies

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.

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