  We prove that the solution of certain linear stochastic differential
equations in Hilbert spaces, namely those with bounded operators as well as the
conservative stochastic Schr\"odinger equations, can be obtained - along the
lines of the Lie-Trotter product formula from semigroup theory - by splitting
the equation into a ``deterministic'' and a ``stochastic'' part and alternately
applying the corresponding solution flows in an iterative manner to the initial
value.
