Stability for Hawkes processes with inhibition

Multivariate Hawkes processes on inhomogeneous random graphs

“…The litterature on mean-field analysis is huge and does not restrict to neuroscience applications (see the following references as far as neurosciences are concerned: integrate and fire models [22], PDMP [48,19]). As for mean-field Hawkes processes, similar models have been considered in [23,36,38] and expanded with additional features (age dependence in [14,59], inhibition in [20,30,60]). What makes the mean-field analysis for Hawkes processes particularly tractable is that the large population limit is given in terms of an inhomogeneous Poisson process whose intensity solves a convolution equation [23].…”