  This paper contains a study of multivariate second order stochastic mappings
indexed by an abstract set $\Lambda$ in close connection to their operator
covariance functions. The characterizations of the normal Hilbert module or of
Hilbert spaces associated to such a multivariate second order stochastic
mapping in terms of reproducing kernel structures are given, aiming not only to
gather into a unified way some concepts from the field, but also to indicate an
instrument for extending the very well elaborated theory of multivariate second
order stochastic processes (or random fields) to the case of multivariate
second order random distribution fields, including multivariate second order
stochastic measures. In particular a general Wold type decomposition is
extended and discussed in our framework.
