Subordinated Random Fields: Construction of Self-similar Fields

Abstract

We give a complete characterization of the so-called subordinated random fields of a stationary Gaussian random field. This result enables us to construct new, non-trivial (subordinated) self-similar random fields, i.e. such random fields which may appear as the limit random field in limit theorems. To tell whether the formulas defining these subordinated random fields are meaningful or not we have to decide whether certain classical integrals are convergent or divergent. Hence this chapter contains some results in this direction.