Euclidean random fields obtained by convolution from generalized white noise

Abstract

We study Euclidean random fields X over Rd of the form X=G*F, where F is a generalized white noise over Rd and G is an integral kernel. We give conditions for the existence of the characteristic functional and moment functions and we construct a convergent lattice approximation of X. Finally, we perform the analytic continuation of the moment functions and the characteristic functional of X, obtaining the corresponding relativistic functions on Minkowski space.