  We introduce the notion of perturbations of quantum stochastic models using
the series product, and establish the asymptotic convergence of sequences of
quantum stochastic models under the assumption that they are related via a
right series product perturbation. While the perturbing models converge to the
trivial model, we allow that the individual sequences may be divergent
corresponding to large model parameter regimes that frequently occur in
physical applications. This allows us to introduce the concept of
asymptotically equivalent models, and we provide several examples where we
replace one sequence of models with an equivalent one tailored to capture
specific features. These examples include: a series product formulation of the
principle of virtual work; essential commutativity of the noise in strong
squeezing models; the decoupling of polarization channels in scattering by
Faraday rotation driven by a strong laser field; and an application to quantum
local asymptotic normality.
