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An extension of the Wong-Zakai theorem for stochastic evolution equations in Hilbert spaces. (English) Zbl 0754.60060
Summary: We examine an approximation theorem of the Wong-Zakai type for stochastic evolution equations in a Hilbert space with the noise being the generalized derivative of the Wiener process with values in another Hilbert space. As a consequence of the approximation of the Wiener process we get in the limit equation the Itô correction term for the infinite-dimensional case. The obtained result includes the case of stochastic delay equations. The uniqueness and existence of solutions are guaranteed by known theorems for the mild solutions.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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