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

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2008, Volume 11, Number 2, Pages 201–218 (Mi sjvm43)

This article is cited in 17 scientific papers (total in 17 papers)

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

S. M. Prigarin^a, K. Hahn^b, G. Winkler^b

^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

Full-text PDF (791 kB) Citations (17)

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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.

Received: 08.02.2007

English version:
Numerical Analysis and Applications, 2008, Volume 1, Issue 2, Pages 163–178
DOI: https://doi.org/10.1134/S1995423908020079

MSC: 28A80, 62M10, 65C05

Language: Russian

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

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\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

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\transl

\jour Num. Anal. Appl.

\yr 2008

\vol 1

\issue 2

\pages 163--178

\crossref{https://doi.org/10.1134/S1995423908020079}

Linking options:

https://www.mathnet.ru/eng/sjvm43

https://www.mathnet.ru/eng/sjvm/v11/i2/p201

This publication is cited in the following 17 articles:

Advances in Chemical and Materials Engineering, Bio-Locomotion Interfaces and Biologization Potential in 4-D Printing, 2024, 203
O. Lazorenko, L. Chernogor, “FRACTAL RADIOPHYSICS. Part 2. FRACTAL AND MULTIFRACTAL ANALYSIS METHODS OF SIGNALS AND PROCESSES”, Radio phys. radio astron., 28:1 (2023), 5
Evangelina García-Armenta, Gustavo F. Gutiérrez-López, “Fractal Microstructure of Foods”, Food Eng Rev, 14:1 (2022), 1
Tetiana Ianevych, Iryna Rozora, Anatolii Pashko, “On one way of modeling a stochastic process with given accuracy and reliability”, Monte Carlo Methods and Applications, 28:2 (2022), 135
Pashko A., Sinyayska O., Oleshko T., “Simulation of Fractional Brownian Motion and Estimation of Hurst Parameter”, 15Th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (Tcset - 2020), IEEE, 2020, 632–637
Pashko A., Krak V I., Vasylyk O., Syniavska O., Puhach V.M., Shevchenko L.S., Omiotek Z., Mussabekova A., Baitussupov D., “Quality Estimation For Models of a Generalized Wiener Process”, Prz. Elektrotechniczny, 96:10 (2020), 94–97
Nayak S.R., Mishra J., Palai G., “Analysing Roughness of Surface Through Fractal Dimension: a Review”, Image Vis. Comput., 89 (2019), 21–34
Anatolii Pashko, Violeta Tretynyk, 2019 IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S&T), 2019, 855
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
Yuriy Kozachenko, Anatolii Pashko, Olga Vasylyk, “Simulation of generalized fractional Brownian motion in C([0,T])”, Monte Carlo Methods and Applications, 24:3 (2018), 179
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
V. A. Ogorodnikov, S. M. Prigarin, A. S. Rodionov, “Quasi-Gaussian model of network traffic”, Autom. Remote Control, 71:3 (2010), 473–485
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
Lopes R., Betrouni N., “Fractal and multifractal analysis: A review”, Medical Image Analysis, 13:4 (2009), 634–649
Prigarin S.M., Konstantinov P.V., “Spectral numerical models of fractional Brownian motion”, Russian J. Numer. Anal. Math. Modelling, 24:3 (2009), 279–295
S. M. Prigarin, K. Hahn, G. Winkler, “Variational dimension of random sequences and its application”, Num. Anal. Appl., 2:4 (2009), 352–363
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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