  We study the existence of the stochastic flow associated to a linear
stochastic evolution equation $$d X= AX\,d t +\sum_{k} B_k X\,d W_k, $$ on a
Hilbert space. Our first result covers the case where $A$ is the generator of a
$C_0$-semigroup, and $(B_k)$ is a sequence of bounded linear operators such
that $\sum_k\|B_k\|<+\infty$. We also provide sufficient conditions for the
existence of stochastic flows in the Schatten classes beyond the space of
Hilbert-Schmidt operators. Some new results and examples concerning the
so-called commutative case are presented as well.
