Stochastic integration for inhomogeneous Wiener process in the dual of a nuclear space (Q753271)

Let E be a nuclear space and F be a locally convex space, whose topology is generated by a family of Hilbert-seminorms. Let W denote a generalized Wiener process with values in \(E'\) (the dual of E), i.e. a not necessarily time-homogeneous E-valued Gaussian process with independent increments. In the present paper a stochastic integral relative to W is constructed. The integrands are operator-valued processes X with \(X_ s(\omega)\in L(E'_ s,F')\), \(E'_ s\) being a Hilbert subspace of E. The paper extends former results of the authors, where they considered homogeneous Wiener processes as integrators. Finally, it is proved that under rather weak assumptions a given generalized Wiener process is necessarily a stochastic integral with respect to a time-homogeneous Wiener process.