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Article overview
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Strong uniqueness for stochastic evolution equations in Hilbert spaces with bounded measurable drift | G. Da Prato
; F. Flandoli
; E. Priola
; M. Röckner
; | Date: |
2 Sep 2011 | Abstract: | We prove pathwise (hence strong) uniqueness of solutions to stochastic
evolution equations in Hilbert spaces with merely measurable bounded drift and
cylindrical Wiener noise, thus generalizing Veretennikov’s fundamental result
on $R^d$ to infinite dimensions. Because Sobolev regularity results implying
continuity or smoothness of functions, do not hold on infinite dimensional
spaces, we employ methods and results developed in the study of
Malliavin-Sobolev spaces in infinite dimensions. The price we pay is that we
can prove uniqueness for a large class, but not for every initial distribution.
Such restriction, however, is common in infinite dimensions. | Source: | arXiv, 1109.0363 | Services: | Forum | Review | PDF | Favorites |
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