A deformation/blurring-based spatio-temporal model |
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Authors: | J. M. Angulo A. E. Madrid |
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Affiliation: | 1. Department of Statistics and Operations Research, Faculty of Sciences, University of Granada, Campus Fuente Nueva s/n, 18071, Granada, Spain 2. University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, C/Coronel López Pe?a, s/n, 30720, Santiago de la Ribera, Murcia, Spain
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Abstract: | A key objective in spatio-temporal modeling consists of providing an appropriate representation of complexity in interactive spatio-temporal dynamics inherent to real phenomena. Propagated effect of dynamical spatial deformation provides a meaningful way to describe certain forms of heterogeneous behaviour; in particular, in relation to processes evolving in unstable media, or to account for the possible effect of covariates, to mention some significant interpretations. In this paper, the formulation of a discrete time and continuous space spatio-temporal interaction model with autoregressive dynamics, incorporating the effect of continuous deformation of the spatial support over time, is studied. Among other fields, this approach provides a suitable representation for a variety of geophysical and environmental applications. In particular, a vast family of heterogeneous models is generated from models which display homogeneity in the absence of deformation. Structural characteristics and variability properties, as well as self-consistency conditions for a limiting continuous-time approximation, are analyzed. |
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