  We study the dependence of mild solutions to linear stochastic evolution
equations on Hilbert space driven by Wiener noise, with drift having linear
part of the type $A+\varepsilon G$, on the parameter $\varepsilon$. In
particular, we study the limit and the asymptotic expansions in powers of
$\varepsilon$ of these solutions, as well as of functionals thereof, as
$\varepsilon \to 0$, with good control on the remainder. These convergence and
series expansion results are then applied to a parabolic perturbation of the
Musiela SPDE of mathematical finance modeling the dynamics of forward rates.
