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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Infinite Dimensional Stochastic Cauchy Problems in Ito and Differential Forms: Comparison of Solutions
verfasst von : Irina V. Melnikova, Olga Starkova
Erschienen in: Current Trends in Analysis and Its Applications
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Abstract
We consider three types of solutions to the infinite dimensional stochastic Cauchy problem \(X'(t)=AX(t)+B{\mathbb{W}}(t)\), t≥0, X(0)=ζ, with A being the generator of a regularized semigroup in a Hilbert space and a white noise \({\mathbb{W}}\) in another Hilbert space: weak, generalized in t, and generalized in a random variable. It is proved coincidence of the solutions under the conditions they exist.