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Spatial Hurst–Kolmogorov Clustering

Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 9, 157 80 Zographou, Greece
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Academic Editors: Raffaele Barretta and Francesc Pozo Montero
Encyclopedia 2021, 1(4), 1010-1025; https://doi.org/10.3390/encyclopedia1040077
Received: 15 January 2021 / Revised: 3 May 2021 / Accepted: 9 September 2021 / Published: 29 September 2021
(This article belongs to the Section Engineering)
The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale. View Full-Text
Keywords: stochastic analysis; scale domain; Hurst–Kolmogorov dynamics; spatio-temporal clustering; climacogram stochastic analysis; scale domain; Hurst–Kolmogorov dynamics; spatio-temporal clustering; climacogram
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MDPI and ACS Style

Dimitriadis, P.; Iliopoulou, T.; Sargentis, G.-F.; Koutsoyiannis, D. Spatial Hurst–Kolmogorov Clustering. Encyclopedia 2021, 1, 1010-1025. https://doi.org/10.3390/encyclopedia1040077

AMA Style

Dimitriadis P, Iliopoulou T, Sargentis G-F, Koutsoyiannis D. Spatial Hurst–Kolmogorov Clustering. Encyclopedia. 2021; 1(4):1010-1025. https://doi.org/10.3390/encyclopedia1040077

Chicago/Turabian Style

Dimitriadis, Panayiotis, Theano Iliopoulou, G.-Fivos Sargentis, and Demetris Koutsoyiannis. 2021. "Spatial Hurst–Kolmogorov Clustering" Encyclopedia 1, no. 4: 1010-1025. https://doi.org/10.3390/encyclopedia1040077

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