HIDA DISTRIBUTION CONSTRUCTION OF NON-GAUSSIAN REFLECTION POSITIVE GENERALIZED RANDOM FIELDS

Multiple stochastic integrals with respect to the Gaussian white noise indexed by R-d are used for the construction of reflection positive non-Gaussian S'(Rd) valued random variables (random fields). This construction is then extended to a class of Hida distribution to consider several interesting examples. In particular, some new fields (without full Euclidean invariance but satisfying all other axioms, including space rotation invariance) are constructed through this probabilistic (and purely Euclidean) procedure.