Stochastic integration for inhomogeneous Wiener process in the dual of a nuclear space

A stochastic integral with respect to a generalized, i.e., not necessarily time-homogeneous, Wiener process in the dual of a nuclear space is defined. The integrands are random linear operators X = (Xs)s[set membership, variant]R+, with values in the dual of a multi-Hilbertian space, the domain of Xs depending in general on s. As an application of this result we prove that, under weak and natural assumptions, a generalized Wiener process can be represented in the strong sense as the stochastic integral with respect to another Wiener process, whose covariance functional is given in advance, in particular, with respect to a homogeneous Wiener process.