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Large-scale behavior of a wide class of spatial and spatiotemporal processesis characterized in terms of informational measures. Specifically, subordinatedrandom fields defined by non-linear transformations on the family ofhomogeneous and isotropic Lancaster-Sarmanov random fields are studied underlong-range dependence (LRD) assumptions. In the spatial case, it is shown thatShannon mutual information beween marginal distributions for infinitelyincreasing distance, which can be properly interpreted as a measure ofmacroscale structural complexity and diversity, has an asymptotic power decaythat directly depends on the underlying LRD parameter, scaled by thesubordinating function rank. Sensitivity with respect to distortion induced bythe deformation parameter under the generalized form given by divergence-basedR\'enyi mutual information is also analyzed. In the spatiotemporal framework, aspatial infinite-dimensional random field approach is adopted. The study of thelarge-scale asymptotic behavior is then extended under the proposal of afunctional formulation of the Lancaster-Sarmanov random field class, as well asof divergence-based mutual information. Results are illustrated, in the contextof geometrical analysis of sample paths, considering some scenarios based onGaussian and Chi-Square subordinated spatial and spatio-temporal random fields.

Macroscale structural complexity analysis of subordinated spatiotemporal random fields