Stochastic mappings and random distribution fields III. Module propagators and uniformly bounded linear stationarity

In this paper, the third in our sequence of papers on multivariate stochastic mappings, we focus on the type of, not necessarily stationary, stochastic mappings that are representable with the aid of a certain operator semigroup, called module propagator. As in the previous papers we obtain neater results for multivariate second order random distribution fields, from which the main result regards the extension to this setting of the theory of uniformly bounded linearly stationary random fields.