  In this paper we study well-posedness of a class of semi-linear abstract
stochastic evolution equations in a Hilbert space $H$. Here the non-linear term
is an application $G=F\circ \mathscr{C}$, where $F: H\to H$ is a Lipschitz
function while $\mathscr{C}:D(\mathscr{C})\subset H\to H$ is a linear unbounded
operator on $H$. The fact that $G$ is not a Lipschitz function offers many
difficulties in applying the usual methods of perturbation in stochastic
analysis and thus makes the study interesting. Our approach is new and it is
based on the concept of Yosida extension of admissible observation operators,
and allows us to introduce a new concept of solutions for such stochastic
equations. Furthermore, we prove the Feller property for the corresponding
transition semigroup. Finally, we give an application to a general class of
semilinear neutral stochastic equations.
