  We develop a general approach to Stein's method for approximating a random
process in the path space $D([0,T]\to R^d)$ by a real continuous Gaussian
process. We then use the approach in the context of processes that have a
representation as integrals with respect to anunderlying point process,
deriving a general quantitative Gaussian approximation. The error bound is
expressed in terms of couplings of the original process to processes generated
from the reduced Palm measures associated with the point process. As
applications, we study certain $\text{GI}/\text{GI}/\infty$ queues in the
"heavy traffic" regime.
