Geodesic
The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 251-267

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We study the existence, uniqueness, and stability of a solution to the Cauchy problem for a stochastic differential equation with multiplicative noise in the spaces of generalized random variables with values in a Hilbert space.
Keywords: Cauchy problem, semigroup, white noise, generalized solutions. 
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I. V. Melnikova; M. A. Alshanskiy. The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 251-267. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a19/