  This paper is interested in semilinear stochastic equations having unbounded
nonlinear perturbations in the deterministic part and/or in the random part.
Moreover, the linear part of these equations is governed by a not necessarily
analytic semigroup. The main difficulty with these equations is how to define
the concept of mild solutions due to the chosen type of unbounded
perturbations. To overcome this problem, we first proved a regularity property
of the stochastic convolution with respect to the domain of "admissible"
unbounded linear operators (not necessarily closed or closable). This is done
using Yosida extensions of such unbounded linear operators. After proving the
well-posedness of these equations, we also establish the Feller property for
the corresponding transition semigroups. Several examples like heat equations
and schr\"odinger equations with nonlocal perturbations terms are given.
Finally, we give an application to a general class of semilinear neutral
stochastic equations.
