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 non-linear 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 beween marginal distributions for infinitely increasing distance, which can be properly interpreted as a measure of macroscale structural complexity and diversity, has an asymptotic power decay that directly 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 R\'enyi 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 spatio-temporal random fields.

翻译：信息计量是广泛空间和空间时空进程的大规模大规模行为特征。具体地说,在长距离依赖(LRD)假设下,研究由同质和异端Lancaster-Sarmanov家庭非线性变异定义的非线性变异所定义的附属随机字段。在空间假设中,显示香农相互信息为无限扩大的距离进行边际分布,可被适当解释为宏观结构复杂性和多样性的计量,其衰减直接取决于根基LRD参数,以次调函数等级为尺度。还分析了对基于差异的R\'enyi相互信息以普遍形式呈现的变形参数引起的变形的感知性。在空间假设框架中,采用了空间无限的无线随机场方法。然后,根据兰开斯特-Sarmanov随机场级的功能配置建议,扩展了大规模变形行为的研究,以及一些基于差异的相互信息。在基于空间空间图象和空间平流场的草率分析中展示了结果。