Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
"Compound Poisson process approximation." Ann. Probab. 30 (3) 1492 - 1537, July 2002. https://doi.org/10.1214/aop/1029867135