  We investigate the asymptotic behaviour of networks of interacting non-linear
Hawkes processes modeling a homogeneous population of neurons in the large
population limit. In particular, we prove a functional central limit theorem
for the mean spike-activity thereby characterizing the asymptotic fluctuations
in terms of a stochastic Volterra integral equation. Our approach differs from
previous approaches in making use of the associated resolvent in order to
represent the fluctutations as Skorokhod continuous mappings of weakly
converging martingales. Since the Lipschitz properties of the resolvent are
explicit, our analysis in principle also allows to derive approximation errors
in terms of driving martingales.
