Pathwise uniqueness for a class of SDE in Hilbert spaces and applications

An abstract evolution equation in Hilbert spaces is considered. In the deterministic case, it includes several examples of non-uniqueness. It is proved that pathwise uniqueness is restored by means of a suitably non-degenerate additive noise. The proof is based on the associated infinite dimensional...

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Bibliographic Details
Published in:Journal of functional analysis 2010-07, Vol.259 (1), p.243-267
Main Authors: Da Prato, G., Flandoli, F.
Format: Article
Language:English
Subjects:
Infinite dimensional Kolmogorov equations
Pathwise uniqueness
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Summary:An abstract evolution equation in Hilbert spaces is considered. In the deterministic case, it includes several examples of non-uniqueness. It is proved that pathwise uniqueness is restored by means of a suitably non-degenerate additive noise. The proof is based on the associated infinite dimensional Kolmogorov equation.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2009.11.019