Non-Gaussian Complex Random Fields, their Skeletons and Path Measures

Abstract

This work investigates complex random fields Z, which have a rotation invariant path measure. Fields of this type are constructed and analyzed in terms of (pathwise convergent) L 2-expansions, and quasi invariance properties of their path measures are studied. The results are used to investigate ℋL 2(Z), the space of holomorphic L 2-functionals of Z. Conditions are given such that every F∈ℋL 2(Z) admits an L 2-power series expansion, and a general skeleton theorem is proved, which justifies the notion ‘holomorphic’.