We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main theorem, whi
ch is based on the Trotter-Kato theorem, is not restricted to a specific noise model and does not require boundedness of the limit coefficients.
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular
perturbations are obtained. The results are illustrated in several examples of physical interest.