A Review of Basic FCLT’s

We briefly review Donsker’s functional central limit theorem (FCLT), which is a generalization of the classic central limit theorem (CLT). We then review FCLT’s for renewal processes and renewalreward processes and their generalization to other counting processes and random sums. We show how to apply the continuous mapping and generalizations that preserve convergence in the function space D. These methods have played an important role in establishing heavy-traffic limits for queueing models.