Fluctuation limits for mean-field interacting nonlinear Hawkes processes

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