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Sib. Zh. Vychisl. Mat., 2008, Volume 11, Number 2, Pages 201–218 (Mi sjvm43)  

This article is cited in 9 scientific papers (total in 9 papers)

Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion

S. M. Prigarina, K. Hahnb, G. Winklerb

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
b Institute of Biomathematics and Biometry Helmholtz Zentrum München

Abstract: The objective of the paper is to study by Monte Carlo simulation statistical properties of two numerical methods (the extended counting method and the variance counting method) developed to estimate the Hausdorff dimension of a time series and applied to the fractional Brownian motion.

Key words: fractal set, Hausdorff dimension, extended counting method, variance counting method, generalized Wiener process, fractional Brownian motion.

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English version:
Numerical Analysis and Applications, 2008, 1:2, 163–178

MSC: 28A80, 62M10, 65C05
Received: 08.02.2007

Citation: S. M. Prigarin, K. Hahn, G. Winkler, “Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion”, Sib. Zh. Vychisl. Mat., 11:2 (2008), 201–218; Num. Anal. Appl., 1:2 (2008), 163–178

Citation in format AMSBIB
\by S.~M.~Prigarin, K.~Hahn, G.~Winkler
\paper Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion
\jour Sib. Zh. Vychisl. Mat.
\yr 2008
\vol 11
\issue 2
\pages 201--218
\jour Num. Anal. Appl.
\yr 2008
\vol 1
\issue 2
\pages 163--178

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    This publication is cited in the following articles:
    1. Belov S.D., Lomakin S.V., Ogorodnikov V.A., Prigarin S.M., Rodionov A.S., Chubarov L.B., “Analiz i modelirovanie trafika v vysokoproizvoditelnykh kompyuternykh setyakh”, Vestn. Novosibirskogo gos. un-ta. Ser.: Informatsionnye tekhnologii, 6:2 (2008), 41–48
    2. Lopes R., Betrouni N., “Fractal and multifractal analysis: A review”, Medical Image Analysis, 13:4 (2009), 634–649  crossref  isi  scopus
    3. Prigarin S.M., Konstantinov P.V., “Spectral numerical models of fractional Brownian motion”, Russian J. Numer. Anal. Math. Modelling, 24:3 (2009), 279–295  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. M. Prigarin, K. Hahn, G. Winkler, “Variational dimension of random sequences and its application”, Num. Anal. Appl., 2:4 (2009), 352–363  mathnet  crossref
    5. V. A. Ogorodnikov, S. M. Prigarin, A. S. Rodionov, “Quasi-Gaussian model of network traffic”, Autom. Remote Control, 71:3 (2010), 473–485  mathnet  crossref  mathscinet  zmath  isi
    6. Lopes R., Dubois P., Bhouri I., Akkari-Bettaieb H., Maouche S., Betrouni N., “La géométrie fractale pour l'analyse de signaux médicaux: état de l'art [Fractal geometry for medical signal analysis: A review]”, IRBM, 31:4 (2010), 189–208  crossref  isi  scopus
    7. Hahn K., Massopust P.R., Prigarin S., “a New Method To Measure Complexity in Binary Or Weighted Networks and Applications To Functional Connectivity in the Human Brain”, BMC Bioinformatics, 17 (2016), 87  crossref  isi  scopus
    8. A. O. Pashko, O. I. Vasylyk, “Simulation of fractional Brownian motion basing on its spectral representation”, Theory Stoch. Process., 23(39):1 (2018), 73–81  mathnet  mathscinet  zmath
    9. Nayak S.R., Mishra J., Palai G., “Analysing Roughness of Surface Through Fractal Dimension: a Review”, Image Vis. Comput., 89 (2019), 21–34  crossref  isi  scopus
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