Mean field limits for interacting Hawkes processes in a diffusive regime

This is a seminar presented by Dr. Dasha Loukianova (University of Evry-Paris Saclay)

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime.

The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random measures. We show that, as the number of interacting components N tends to infinity, this intensity converges in distribution in Skorohod space to a CIR-type diffusion. Moreover, we prove the convergence in distribution of the Hawkes processes to the limit point process having the limit diffusion as intensity. To prove the convergence results, we use analytical technics based on the convergence of the associated infinitesimal generators and Markovian semigroups..

This is a joint work with Xavier Erny and Eva Löcherbach.

If you are interested to join this talk, please contact Dr Miryana Grigorova at for the Zoom details.