Random Fields

Abstract

We consider material on random fields because some of the questions posed are natural in the context of random fields. Our discussion will generally follow that of Georgii 1988. The parameter set of the random variables x₁ i ∈ S is a countable infinite set. A typical case would be that in which S is the set of k-dimensional lattice points. The random variables x _i take values in a measure space (E, ε) with ε a σ7-field of subsets of E. E could be countable or a continuous state space like R^d with ε the σ-fieid of Borel subsets of R^d with d a positive integer. The random variables (x _i ) _∈s are defined on a probability space (ΩF, µ).