Spatial Hurst–Kolmogorov Clustering

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

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[English]

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.