Regularized and generalized solutions of infinite-dimensional stochastic problems

The paper is concerned with solutions of Cauchy's problem for stochastic differential-operator equations in separable Hilbert spaces. Special emphasis is placed on the case when the operator coefficient of the equation is not a generator of a C0-class semigroup, but rather generates some regularized semigroup. Regularized solutions of equations in the Itô form with a Wiener process as an inhomogeneity and generalized solutions of equations with white noise are constructed in various spaces of abstract distributions. Bibliography: 23 titles.