  We consider the effect of perturbations to a quasi-linear parabolic
stochastic differential equation set in a UMD Banach space $X$. To be precise,
we consider perturbations of the linear part, i.e. the term concerning a linear
operator $A$ generating an analytic semigroup. We provide estimates for the
difference between the solution to the original equation $U$ and the solution
to the perturbed equation $U_0$ in the $L^p(\Omega;C([0,T];X))$-norm. In
particular, this difference can be estimated $|| R(\lambda:A)-R(\lambda:A_0)
||$ for sufficiently smooth non-linear terms. The work is inspired by the
desire to prove convergence of space discretization schemes for such equations.
In this article we prove convergence rates for the case that $A$ is
approximated by its Yosida approximation, and in a forthcoming publication we
consider convergence of Galerkin and finite-element schemes in the case that
$X$ is a Hilbert space.
