an:05553448
Zbl 1165.47031
Da Prato, Giuseppe; R??ckner, Michael
Erratum: Singular dissipative stochastic equations in Hilbert spaces
EN
Probab. Theory Relat. Fields 143, No. 3-4, 659-664 (2009).
00244580
2009
j
47D07 35K90 60H15
errata
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.
Ren?? L. Schilling (Dresden)
Zbl 1036.47029