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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
Author to whom correspondence should be addressed.
Academic Editors: Raffaele Barretta and Francesc Pozo Montero
Encyclopedia 2021, 1(4), 1010-1025;
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.

AMA Style

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

Chicago/Turabian Style

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

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