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Erratum: Singular dissipative stochastic equations in Hilbert spaces. (English) Zbl 1165.47031
The authors’ paper [Probab. Theory Relat. Fields 124, No. 2, 261–303 (2002; Zbl 1036.47029)] contains an error in the proof of Lemma 5.5; this affects mainly Theorem 7.4 and Proposition 7.2. In this erratum, an alternative proof of Proposition 7.2 is given and Theorem 7.4 is corrected. For this, the authors have to assume a further condition, namely that \[ \lim_{m\to\infty} mR_m f_k = f_k \quad\text{uniformly on \(H_0\) for all \(k\in\mathbb N\)}. \] It is pointed out that this condition is nontrivial and often quite hard to check.
The authors also indicate a misprint in the statement of Lemma 5.6: if \(\dim H=\infty\), path continuity at \(t=0\) is to be understood in the \(\tau_{S_2}\) topology.

47D07 Markov semigroups and applications to diffusion processes
35K90 Abstract parabolic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
Full Text: DOI
[1] Da Prato G., Röckner M.: Singular dissipative stochastic equations in Hilbert spaces. Probab. Theory Relat. Fields 124(2), 261–303 (2002) [MR MR1936019 (2003k:60151)] · Zbl 1036.47029 · doi:10.1007/s004400200214
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