Gaussian white noise with trajectories in the space S′(H)

In this paper we construct a Gaussian white noise with trajectories in the space of generalized functions over S with values in a separable Hilbert space H. We obtain a solution to the Cauchy problem for a linear differential-operator equation with additive white noise as a generalized random process with trajectories in the space of exponential distributions. We prove the existence of a solution in the case when the operator coefficient A generates a C 0-semigroup and in the case when A generates an integrated semigroup.