@misc{10481/91388,
year = {2023},
month = {9},
url = {https://hdl.handle.net/10481/91388},
abstract = {Large-scale behavior of a wide class of spatial and spatiotemporal processes is characterized in terms of informational
measures. Specifically, subordinated random fields defined by nonlinear transformations on the family of homogeneous and
isotropic Lancaster–Sarmanov random fields are studied under long-range dependence (LRD) assumptions. In the spatial
case, it is shown that Shannon mutual information between random field components for infinitely increasing distance,
which can be properly interpreted as a measure of large scale structural complexity and diversity, has an asymptotic power
law decay that depends on the underlying LRD parameter scaled by the subordinating function rank. Sensitivity with
respect to distortion induced by the deformation parameter under the generalized form given by divergence-based Re´nyi
mutual information is also analyzed. In the spatiotemporal framework, a spatial infinite-dimensional random field approach
is adopted. The study of the large-scale asymptotic behavior is then extended under the proposal of a functional formulation
of the Lancaster–Sarmanov random field class, as well as of divergence-based mutual information. Results are
illustrated, in the context of geometrical analysis of sample paths, considering some scenarios based on Gaussian and Chi-
Square subordinated spatial and spatiotemporal random fields.},
organization = {Grants PID2021-128077NB-I00, PGC2018-098860-B-I00, PID2022-142900NB-I00, and PGC2018-099549-B-I00 funded by MCIN /AEI/10.13039/501100011033 / ERDF A way of making Europe, EU},
organization = {Grant CEX2020-001105-M funded by MCIN / AEI/10.13039/
501100011033},
organization = {Funding for open access publishing: Universidad de Granada/
CBUA.},
publisher = {Springer Nature},
keywords = {Lancaster–Sarmanov random field models},
keywords = {Subordinated random fields},
keywords = {Information measures},
title = {Informational assessment of large scale self-similarity in nonlinear random field models},
doi = {10.1007/s00477-023-02541-x},
author = {Angulo Ibáñez, José Miguel and Ruiz Medina, María Dolores},
}