On a class of space-time intrinsic random functions

TL;DR

This paper extends power law generalized covariance functions to spatial-temporal processes, allowing different smoothness in space and time while preserving key properties like explicit series expansions.

Contribution

It introduces a new class of covariance functions for spatial-temporal random fields with differing spatial and temporal smoothness.

Findings

Provides explicit series expansions for the new covariance functions

Ensures the covariance functions maintain desirable mathematical properties

Enhances modeling flexibility for spatial-temporal data

Abstract

Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the degree of smoothness in space and in time may differ while maintaining other desirable properties for the covariance functions, including the availability of explicit convergent and asymptotic series expansions.