Geodesic
Regularized and generalized solutions of infinite-dimensional stochastic problems
Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1565-1592

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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 $C_0$-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.
Keywords: regularized semigroup of operators, abstract distribution, generalized solution, Wiener process, white noise. 
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M. A. Alshanskiy; I. V. Mel'nikova. Regularized and generalized solutions of infinite-dimensional stochastic problems. Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1565-1592. http://geodesic.mathdoc.fr/item/SM_2011_202_11_a0/